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Abraham Robinson, 1918-1974


Author: Angus J. Macintyre
Journal: Bull. Amer. Math. Soc. 83 (1977), 646-666
MathSciNet review: 0532706
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  • 1. Abraham Robinson, On the independence of the axiom of definiteness, J. Symbolic Logic 4 (1939), 69-72.
  • 2. Abraham Robinson, On a certain variation of the distributive law for a commutative algebraic field, Proc. Roy. Soc. Edinburgh. Sect. A. 61 (1941), 93–101. MR 0005104
  • 3. Abraham Robinson, (with S. V. Fagg and P. E. Montagnon), Note on the interpretation of V-g recorders, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2097, 1945.
  • 4. Abraham Robinson, The aerodynamic loading of wings with endplates, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2342, 1945/1950.
  • 5. Abraham Robinson, Shock transmission in beams, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2265, 1945/1950.
  • 6. Abraham Robinson, The wave drag of diamond-shaped aerofoils at zero incidence, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2394, 1946/1950.
  • 7. A. Robinson, Aerofoil theory of a flat delta wing at supersonic speeds, Rep. and Memoranda no. 2548 (10,222), Ministry of Supply [London], Aeronaut. Res. Council, 1952. MR 0052945
  • 8. Th. Motzkin and A. Robinson, The characterization of algebraic plane curves, Duke Math. J. 14 (1947), 837–853. MR 0023556
  • 9. A. Robinson and A. D. Young, Note on the application of the linearised theory for compressible flow to transonic speeds, Coll. Aeronaut. Cranfield. Rep. 1947 (1947), no. 2, 7 pp. (2 plates). MR 0024290
  • 10. Abraham Robinson, (with F. T. Davies), The effect of the sweepback of delta wings on the performance of an aircraft at supersonic speeds, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2476, 1947/1951.
  • 11. S. Kirkby and A. Robinson, Interference on a wing due to a body at supersonic speeds, Rep. and Memoranda no. 2500 (10,631), Ministry of Supply [London], Aeronaut. Res. Council, 1952. MR 0047472
  • 12. Abraham Robinson, (with J. H. Hunter-Tod), Bound and trailing vortices in the linearised theory of supersonic flow, and the downwash in the wake of a delta wing, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2409, 1947/1952. MR 14, 219.
  • 13. A. Robinson, On some problems of unsteady supersonic aerofoil theory, Proc. Seventh Internat. Congress Appl. Mech., v. 2, publisher unknown, 1948, pp. 500–514. MR 0033698
  • 14. A. Robinson, On source and vortex distributions in the linearized theory of steady supersonic flow, Quart. J. Mech. Appl. Math. 1 (1948), 408–432. MR 0028145
  • 15. Abraham Robinson, Rotary derivatives of delta wings at supersonic speeds, J. Royal Aeronautical Soc. 52 (1948), 735-752.
  • 16. Abraham Robinson, (with J. H. Hunter-Tod), The aerodynamic derivatives with respect to sideslip for a delta wing with small dihedral at zero incidence at supersonic speeds, Reports and Memoranda of theAeronautical Research Council of Great Britain No. 2410, 1948/1952.
  • 17. A. Robinson, On non-associative systems, Proc. Edinburgh Math. Soc. (2) 8 (1949), 111–118. MR 0035754
  • 18. A. Robinson, On the integration of hyperbolic differential equations, J. London Math. Soc. 25 (1950), 209–217. MR 0037993
  • 19. A. Robinson, On functional transformations and summability, Proc. London Math. Soc. (2) 52 (1950), 132–160. MR 0037371
  • 20. Abraham Robinson, Les rapports entre le calcul déductif et l’interprétation sémantique d’un système axiomatique, Les méthodes formelles en axiomatique. Colloques Internationaux du Centre National de la Recherche Scientifique, no. 26, Paris, 1950, Centre National de la Recherche Scientifique, Paris, 1953, pp. 35–51; discussion, pp. 51–52 (French). MR 0057202
  • 21. Abraham Robinson, On the application of symbolic logic to algebra, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 1, Amer. Math. Soc., Providence, R. I., 1952, pp. 686–694. MR 0046323
  • 22. A. Robinson, Wave reflexion near a wall, Proc. Cambridge Philos. Soc. 47 (1951), 528–544. MR 0041630
  • 23. Abraham Robinson, On axiomatic systems which possess finite models, Methodos (1951), 140-149.
  • 24. A. Robinson, Aerofoil theory for swallow tail wings of small aspect ratio, Aeronaut. Quart. 4 (1952), 69–82. MR 0049744
  • 25. Abraham Robinson, L’application de la logique formelle aux mathématiques, Applications scientifiques de la logique mathématique (Actes du 2^{𝑒} Colloque International de Logique Mathématique, Paris, 1952), Gauthier-Villars, Paris; E. Nauwelaerts, Louvain, 1954, pp. 51–63; discussion, p. 64 (French). MR 0067824
  • 26. A. Robinson, Non-uniform supersonic flow, Quart. Appl. Math. 10 (1953), 307–319. MR 0051657
  • 27. Abraham Robinson, Flow around compound lifting units, Sympos. on High Speed Aerodynamics, Ottawa, Canada, (1953), pp. 26-29.
  • 28. G. G. Lorentz and A. Robinson, Core-consistency and total inclusion for methods of summability, Canadian J. Math. 6 (1954), 27–34. MR 0060041
  • 29. A. Robinson, On some problems of unsteady aerofoil theory, Proceedings of the Second Canadian Symposium on Aerodynamics, Toronto, 1954, The Institute of Aerophysics University of Toronto, Toronto, 1954, pp. 106–122. MR 0072607
  • 30. Abraham Robinson, On predicates in algebraically closed fields, J. Symbolic Logic 19 (1954), 103–114. MR 0062090
  • 31. A. Robinson, Note on an embedding theorem for algebraic systems, J. London Math. Soc. 30 (1955), 249–252. MR 0073549
  • 32. L. L. Campbell and A. Robinson, Mixed problems for hyperbolic partial differential equations, Proc. London Math. Soc. (3) 5 (1955), 129–147. MR 0070017
  • 33. P. C. Gilmore and A. Robinson, Metamathematical considerations on the relative irreducibility of polynomials, Canad. J. Math. 7 (1955), 483–489. MR 0072088
  • 34. Abraham Robinson, On ordered fields and definite functions, Math. Ann. 130 (1955), 275–271. MR 0075932
  • 35. Abraham Robinson, Further remarks on ordered fields and definite functions, Math. Ann. 130 (1956), 405–409. MR 0078352
  • 36. Abraham Robinson, A result on consistency and its application to the theory of definition, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 47–58. MR 0078307
  • 37. Abraham Robinson, Note on a problem of L. Henkin, J. Symb. Logic 21 (1956), 33–35. MR 0075896
  • 38. Abraham Robinson, Ordered structures and related concepts, Mathematical interpretation of formal systems, North-Holland Publishing Co., Amsterdam, 1955, pp. 51–56. MR 0075153
  • 39. Abraham Robinson, Completeness and persistence in the theory of models, Z. Math. Logik Grundlagen Math. 2 (1956), 15–26. MR 0078313
  • 40. Abraham Robinson, Solution of a problem by Erdös-Gillman-Henriksen, Proc. Amer. Math. Soc. 7 (1956), 908–909. MR 0081265, 10.1090/S0002-9939-1956-0081265-9
  • 41. Abraham Robinson, On the motion of small particles in a potential field of flow, Comm. Pure Appl. Math. 9 (1956), 69–84. MR 0078115
  • 42. A. Robinson, Wave propagation in a heterogeneous elastic medium, J. Math. and Phys. 36 (1957), 210–222. MR 0091040
  • 43. A. Robinson, Transient stresses in beams of variable characteristics, Quart. J. Mech. Appl. Math. 10 (1957), 148–159. MR 0091041
  • 44. A. Robinson, Some problems of definability in the lower predicate calculus, Fund. Math. 44 (1957), 309–329. MR 0091922
  • 45. A. H. Lightstone and A. Robinson, Syntactical transforms, Trans. Amer. Math. Soc. 86 (1957), 220–245. MR 0091246, 10.1090/S0002-9947-1957-0091246-2
  • 46. A. H. Lightstone and A. Robinson, On the representation of Herbrand functions in algebraically closed fields, J. Symb. Logic 22 (1957), 187–204. MR 0098093
  • 47. Abraham Robinson, Relative model-completeness and the elimination of quantifiers, Dialectica 12 (1958), 394–407 (English, with German and French summaries). MR 0102472
  • 48. Abraham Robinson, Outline of an introduction to mathematical logic. I, Canad. Math. Bull. 1 (1958), 41–54. MR 0098668
  • 49. Abraham Robinson, Outline of an introduction to mathematical logic. III, IV, Canad. Math. Bull. 1 (1958), 193–208 2 (1959), 33–42. MR 0107596
  • 50. A. Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 179–204. MR 0112841
  • 51. Abraham Robinson, On the concept of a differentially closed field, Bull. Res. Council Israel Sect. F 8F (1959), 113–128 (1959). MR 0125016
  • 52. Abraham Robinson, Obstructions to arithmetical extension and the theorem of Øś and Suszko, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959), 489–495. MR 0111682
  • 53. A. Robinson, Model theory and non-standard arithmetic, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959) Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 265–302. MR 0142463
  • 54. Abraham Robinson, Local differential algebra, Trans. Amer. Math. Soc. 97 (1960), 427–456. MR 0122815, 10.1090/S0002-9947-1960-0122815-9
  • 55. A. Robinson, On the mechanization of the theory of equations, Bull. Res. Council Israel Sect. F 9F (1960), 47–70 (1960). MR 0147394
  • 56. Abraham Robinson and Elias Zakon, Elementary properties of ordered abelian groups, Trans. Amer. Math. Soc. 96 (1960), 222–236. MR 0114855, 10.1090/S0002-9947-1960-0114855-0
  • 57. Abraham Robinson, Recent developments in model theory, Logic, Methodology and Philosophy of Science (Proc. 1960 Internat. Congr.), Stanford Univ. Press, Stanford, Calif., 1962, pp. 60–79. MR 0167395
  • 58. Abraham Robinson, On the construction of models, Essays on the foundations of mathematics, Magnes Press, Hebrew Univ., Jerusalem, 1961, pp. 207–217. MR 0162719
  • 59. Abraham Robinson, On the D-calculus for linear differential equations with constant coefficients, Math. Gazette 45 (1961), 202-206.
  • 60. Abraham Robinson, Non-standard analysis, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 432–440. MR 0142464
  • 61. A. Robinson, A note on embedding problems, Fund. Math. 50 (1961/1962), 455–461. MR 0139514
  • 62. Abraham Robinson, Aerofoil theory, Handbook of Engineering Mechanics (W. Flugge, editor), McGraw-Hill, New York, 1962, Chap. 72.
  • 63. Abraham Robinson, Modern mathematics and the secondary schools, Internat. Rev. Education 8 (1963), 34-40.
  • 64. A. Robinson, A basis for the mechanization of the theory of equations, Computer programming and formal systems, North-Holland, Aamsterdam, 1963, pp. 95–99. MR 0147395
  • 65. S. Halfin and A. Robinson, Local partial differential algebra, Trans. Amer. Math. Soc. 109 (1963), 165–180. MR 0153673, 10.1090/S0002-9947-1963-0153673-7
  • 66. Abraham Robinson, On languages which are based on non-standard arithmetic, Nagoya Math. J. 22 (1963), 83–117. MR 0153569
  • 67. Abraham Robinson, On generalized limits and linear functionals, Pacific J. Math. 14 (1964), 269–283. MR 0164235
  • 68. Calvin C. Elgot and Abraham Robinson, Random-access stored-program machines, an approach to programming languages, J. Assoc. Comput. Mach. 11 (1964), 365–399. MR 0174193
  • 69. Abraham Robinson, Between logic and mathematics, I.C.S.U. Review 6 (1964), 218-226.
  • 70. Abraham Robinson, Formalism 64, Logic, Methodology and Philos. Sci. (Proc. 1964 Internat. Congr.), North-Holland, Amsterdam, 1965, pp. 228–246. MR 0214431
  • 71. Abraham Robinson, On the theory of normal families, Acta Philos. Fenn. Fasc. 18 (1965), 159–184. MR 0188406
  • 72. Allen R. Bernstein and Abraham Robinson, Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific J. Math. 16 (1966), 421–431. MR 0193504
  • 73. Abraham Robinson, A new approach to the theory of algebraic numbers, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 40 (1966), 222–225 (English, with Italian summary). MR 0214455
  • 74. Abraham Robinson, A new approach to the theory of algebraic numbers. II, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 40 (1966), 770–774 (English, with Italian summary). MR 0214456
  • 75. Abraham Robinson, Topics in non-Archimedean mathematics, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 285–298. MR 0197324
  • 76. Abraham Robinson, Non-standard theory of Dedekind rings, Nederl. Akad. Wetensch. Proc. Ser. A 70=Indag. Math. 29 (1967), 444–452. MR 0223351
  • 77. Abraham Robinson, Nonstandard arithmetic, Bull. Amer. Math. Soc. 73 (1967), 818–843. MR 0218231, 10.1090/S0002-9904-1967-11809-3
  • 78. Abraham Robinson, On some applications of model theory to algebra and analysis, Rend. Mat. e Appl. (5) 25 (1966), 562–592. MR 0219406
  • 79. C. C. Elgot, A. Robinson, and J. D. Rutledge, Multiple control computer models, Systems and Computer Science (Proc. Conf., London, Ont., 1965) Univ. Toronto Press, Toronto, Ont., 1967, pp. 60–76. MR 0235770
  • 80. Abraham Robinson, Model theory in contemporary philosophy; a survey. Vol. I, Logic and the Foundation of Mathematics (Kilbansky, editor), Firenze, La Nuova Italia Editrice, 1968, pp. 61-73.
  • 81. Abraham Robinson, Some thoughts on the history of mathematics, Compositio Math. 20 (1968), 188–193 (1963). MR 0224422
  • 82. Abraham Robinson, (with A. E. Hurd), On flexural wave propagation in nonhomogeneous elastic plates, SIAM J. Appl. Math. 16 (1968), 1081-1089.
  • 83. Abraham Robinson, Topics in nonstandard algebraic number theory, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 1–17. MR 0268155
  • 84. Abraham Robinson and Elias Zakon, A set-theoretical characterization of enlargements, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 109–122. MR 0239965
  • 85. Abraham Robinson, Germs, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 138–149. MR 0236427
  • 86. Abraham Robinson, Problems and methods of model theory, Aspects of Math. Logic (C.I.M.E., Varenna, 1968) Edizioni Cremonese, Rome, 1969, pp. 181–266. MR 0260584
  • 87. Abraham Robinson, Elementary embeddings of fields of power series, J. Number Theory 2 (1970), 237–247. MR 0258805
  • 88. Jon Barwise and Abraham Robinson, Completing theories by forcing, Ann. Math. Logic 2 (1970), no. 2, 119–142. MR 0272613
  • 89. Abraham Robinson, Compactification of groups and rings and nonstandard analysis, J. Symbolic Logic 34 (1969), 576–588. MR 0284540
  • 90. Abraham Robinson, Forcing in model theory, Symposia Mathematica, Vol. V (INDAM, Rome, 1969/70) Academic Press, London, 1971, pp. 69–82. MR 0278925
  • 91. Abraham Robinson, Non-standard analysis, A filmed lecture presented by the M.A.A., 1970 (about one hour).
  • 92. Abraham Robinson, Infinite forcing in model theory, Proceedings of the Second Scandinavian Logic Symposium (Oslo, 1970), North-Holland, Amsterdam, 1971, pp. 317–340. Studies in Logic and the Foundations of Mathematics, Vol. 63. MR 0357106
  • 93. Abraham Robinson, Forcing in model theory, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 245–250. MR 0505456
  • 94. Abraham Robinson, On the notion of algebraic closedness for noncommutative groups and fields, J. Symbolic Logic 36 (1971), 441–444. MR 0290949
  • 95. Abraham Robinson, Algebraic function fields and non-standard arithmetic, Contributions to non-standard analysis (Sympos., Oberwolfach, 1970), North-Holland, Amsterdam, 1972, pp. 1–14. Studies in Logic and Found. Math., Vol. 69. MR 0480522
  • 96. Edward R. Fisher and Abraham Robinson, Inductive theories and their forcing companions, Israel J. Math. 12 (1972), 95–107. MR 0314612
  • 97. Abraham Robinson, (with P. J. Kelemen), The nonstandard $łambda :\varphi \sp{4}\sb{2}(x):$ model. I, II, J. Mathematical Phys. 13 (1972), 1875-1878. MR 47 #8016.
  • 98. Abraham Robinson, Function theory on some nonarchimedean fields, Amer. Math. Monthly 80 (1973), no. 6, 87–109. Papers in the foundations of mathematics. MR 0330126
  • 99. Abraham Robinson, (with Donald J. Brown), A limit theorem in the cores of large standard exchange economies, Proc. Nat. Acad. Sci. 69 (1972), 1258-1260.
  • 100. Abraham Robinson, On the real closure of a Hardy field, Theory of sets and topology (in honour of Felix Hausdorff, 1868–1942), VEB Deutsch. Verlag Wissensch., Berlin, 1972, pp. 427–433. MR 0340225
  • 101. A. Robinson, On bounds in the theory of polynomial ideals, Selected questions of algebra and logic (a collection dedicated to the memory of A. I. Mal′cev) (Russian), Izdat. “Nauka” Sibirsk. Otdel., Novosibirsk, 1973, pp. 245–252. MR 0337595
  • 102. Abraham Robinson, Ordered differential fields, J. Combinatorial Theory Ser. A 14 (1973), 324–333. MR 0323768
  • 103. Abraham Robinson, Nonstandard points on algebraic curves, J. Number Theory 5 (1973), 301–327. MR 0396581
  • 104. Abraham Robinson, Metamathematical problems, J. Symbolic Logic 38 (1973), 500–516. MR 0337471
  • 105. Abraham Robinson, A note on topological model theory, Fund. Math. 81 (1973/74), no. 2, 159–171. Collection of articles dedicated to Andrzej Mostowski on the occasion of his sixtieth birthday, II. MR 0342389
  • 106. Abraham Robinson, Standard and nonstandard number systems, Nieuw Arch. Wisk. (3) 21 (1973), 115–133. The Brouwer memorial lecture 1973, Leiden, April 26, 1973. MR 0434803
  • 107. Abraham Robinson, A decision method for elementary algebra and geometry—revisited, Proceedings of the Tarski Symposium (Proc. Sympos. Pure Math., Vol. XXV, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1974, pp. 139–152. MR 0366655
  • 108. Abraham Robinson, Nonstandard arithmetic and generic arithmetic, Logic, methodology and philosophy of science, IV (Proc. Fourth Internat. Congr., Bucharest, 1971) North-Holland, Amsterdam, 1973, pp. 137–154. Studies in Logic and Foundations of Math., Vol. 74. MR 0446966
  • 109. Abraham Robinson, Enlarged sheaves, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Springer, Berlin, 1974, pp. 249–260. Lecture Notes in Math., Vol. 369. MR 0480013
  • 110. Donald J. Brown and Abraham Robinson, The cores of large standard exchange economies, J. Econom. Theory 9 (1974), no. 3, 245–254. MR 0475731
  • 111. Donald J. Brown and Abraham Robinson, Nonstandard exchange economies, Econometrica 43 (1975), 41–55. MR 0443867
  • 112. Abraham Robinson, Concerning progress in the philosophy of mathematics, Logic Colloquium ’73 (Bristol, 1973) North-Holland, Amsterdam, 1975, pp. 41–52. Studies in Logic and the Foundations of Mathematics, Vol. 80. MR 0392492
  • 113. A. Robinson and P. Roquette, On the finiteness theorem of Siegel and Mahler concerning Diophantine equations, J. Number Theory 7 (1975), 121–176. MR 0374022
  • 114. Abraham Robinson, On constrained denotation, Russell Sympos. Duke Univ.
  • 115. D. H. Saracino and V. B. Weispfenning (eds.), Model theory and algebra, Lecture Notes in Mathematics, Vol. 498, Springer-Verlag, Berlin-New York, 1975. A memorial tribute to Abraham Robinson. MR 0387042
  • 116. James Ax and Simon Kochen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605–630. MR 0184930
    James Ax and Simon Kochen, Diophantine problems over local fields. II. A complete set of axioms for 𝑝-adic number theory, Amer. J. Math. 87 (1965), 631–648. MR 0184931
    James Ax and Simon Kochen, Diophantine problems over local fields. III. Decidable fields, Ann. of Math. (2) 83 (1966), 437–456. MR 0201378
    Paul J. Cohen, Decision procedures for real and 𝑝-adic fields, Comm. Pure Appl. Math. 22 (1969), 131–151. MR 0244025
    P. M. Cohn, The embedding of firs in skew fields, Proc. London Math. Soc. (3) 23 (1971), 193–213. MR 0297814
    Paul Eklof and Gabriel Sabbagh, Model-completions and modules, Ann. Math. Logic 2 (1970/1971), no. 3, 251–295. MR 0277372
    Ju. L. Eršov, On elementary theory of maximal normalized fields, Algebra i Logika Sem. 4 (1965), no. 3, 31–70 (Russian). MR 0193086
    Ju. L. Eršov, Fields with a solvable theory, Dokl. Akad. Nauk SSSR 174 (1967), 19–20 (Russian). MR 0214575
    Kurt Gödel, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatsh. Math. Phys. 37 (1930), no. 1, 349–360 (German). MR 1549799, 10.1007/BF01696781
    Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, 10.1007/BF01700692
    Grete Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1926), no. 1, 736–788 (German). MR 1512302, 10.1007/BF01206635
    Joram Hirschfeld and William H. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Mathematics, Vol. 454, Springer-Verlag, Berlin-New York, 1975. MR 0389581
    Irving Kaplansky, Maximal fields with valuations, Duke Math. J. 9 (1942), 303–321. MR 0006161
    Simon Kochen, Integer valued rational functions over the 𝑝-adic numbers: A 𝑝-adic analogue of the theory of real fields, Number Theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967) Amer. Math. Soc., Providence, R.I., 1969, pp. 57–73. MR 0257030
    G. Kreisel, Mathematical significance of consistency proofs, J. Symb. Logic 23 (1958), 155–182. MR 0115912
    Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591
    Serge Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965. MR 0197234
    Peter A. Loeb, Applications of nonstandard analysis to ideal boundaries in potential theory, Israel J. Math. 25 (1976), no. 1-2, 154–187. MR 0457757
    Handbook of mathematical logic, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. Edited by Jon Barwise; With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra; Studies in Logic and the Foundations of Mathematics, Vol. 90. MR 0457132
    Angus Macintyre, On algebraically closed groups, Ann. of Math. (2) 96 (1972), 53–97. MR 0317928
    A. Mal′cev, On a general method for obtaining local theorems in group theory, Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Fak. 1 (1941), no. 1, 3–9 (Russian). MR 0075939
    A. Markoff, On the impossibility of certain algorithms in the theory of associative systems, C. R. (Doklady) Acad. Sci. URSS (N.S.) 55 (1947), 583–586. MR 0020528
    Ju. V. Matijasevič, The Diophantineness of enumerable sets, Dokl. Akad. Nauk SSSR 191 (1970), 279–282 (Russian). MR 0258744
    Michael Morley, Categoricity in power, Trans. Amer. Math. Soc. 114 (1965), 514–538. MR 0175782, 10.1090/S0002-9947-1965-0175782-0
    Christopher Mulvey, Intuitionistic algebra and representations of rings, Recent advances in the representation theory of rings and 𝐶*-algebras by continuous sections (Sem., Tulane Univ., New Orleans, La., 1973), Amer. Math. Soc., Providence, R. I., 1974, pp. 3–57. Mem. Amer. Math. Soc., No. 148. MR 0398799
    P. S. Novikov, On the algorithmic insolvability of the word problem in group theory, American Mathematical Society Translations, Ser 2, Vol. 9, American Mathematical Society, Providence, R. I., 1958, pp. 1–122. MR 0092784
    Emil L. Post, Recursive unsolvability of a problem of Thue, J. Symbolic Logic 12 (1947), 1–11. MR 0020527
    Peter Roquette, Nonstandard aspects of Hilbert’s irreducibility theorem, Model theory and algebra (A memorial tribute to Abraham Robinson), Springer, Berlin, 1975, pp. 231–275. Lecture Notes in Math., Vol. 498. MR 0401771
    Gerald E. Sacks, Saturated model theory, W. A. Benjamin, Inc., Reading, Mass., 1972. Mathematics Lecture Note Series. MR 0398817
    Dana Scott, Boolean models and nonstandard analysis, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos., Pasadena, Calif., 1967) Holt, Rinehart and Winston, New York, 1969, pp. 87–92. MR 0236002
    W. R. Scott, Algebraically closed groups, Proc. Amer. Math. Soc. 2 (1951), 118–121. MR 0040299, 10.1090/S0002-9939-1951-0040299-6
    A. Seidenberg, An elimination theory for differential algebra, Univ. California Publ. Math. (N.S.) 3 (1956), 31–65. MR 0082487
    Saharon Shelah, Uniqueness and characterization of prime models over sets for totally transcendental first-order theories, J. Symbolic Logic 37 (1972), 107–113. MR 0316239
    Saharon Shelah, Differentially closed fields, Israel J. Math. 16 (1973), 314–328. MR 0344116
    Gaisi Takeuti, Boolean valued analysis, Applications of sheaves (Proc. Res. Sympos. Appl. Sheaf Theory to Logic, Algebra and Anal., Univ. Durham, Durham, 1977) Lecture Notes in Math., vol. 753, Springer, Berlin, 1979, pp. 714–731. MR 555569
    Alfred Tarski, A decision method for elementary algebra and geometry, University of California Press, Berkeley and Los Angeles, Calif., 1951. 2nd ed. MR 0044472
    Carol Wood, The model theory of differential fields of characteristic 𝑝̸=0, Proc. Amer. Math. Soc. 40 (1973), 577–584. MR 0329887, 10.1090/S0002-9939-1973-0329887-1
    Carol Wood, Prime model extensions for differential fields of characteristic 𝑝̸=0, J. Symbolic Logic 39 (1974), 469–477. MR 0357109


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1977-14334-6