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ISSN 1088-9485(e) ISSN 0273-0979(p)

Abraham Robinson, 1918-1974

Author(s): Angus J. Macintyre
Journal: Bull. Amer. Math. Soc. 83 (1977), 646-666.
MathSciNet review: 0532706
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R1. Abraham Robinson, On the metamathematics of algebra, North-Holland, Amsterdam, 1951, ix + 195 pp. MR 13, 1715. MR 46322; R2. Abraham Robinson, Théorie métamathématique des ideaux, Gauthier-Villars, Paris; E. Nauwelaerts, Louvain, 1955. MR 16, 1080. MR 69781; R3. Abraham Robinson, (with J. A. Laurmann), Wing theory, Cambridge Univ. Press, 1956. MR 18, 529.; R4. Abraham Robinson, Complete theories, North-Holland, Amsterdam, 1956. MR 17, 817. MR 75897; R5. Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam, 1963, ix + 284 pp.; Russian transl., "Nauka", Moscow, 1967, 376 pp. MR 27 #3533; 36 #3642. MR 220588; R6. Abraham Robinson, Numbers and ideals, Holden-Day, San Francisco, 1965, ix + 106 pp. MR 32 #79. MR 182596; R7. Abraham Robinson, Non-standard analysis, North-Holland, Amsterdam, 1966, xi + 293 pp. MR 34 #5680. MR 205854; R8. Abraham Robinson, (with A. H. Lightstone), Non-Archimedean fields and asymptotic expansions, North-Holland, Amsterdam, 1975.; R9. Abraham Robinson, (with V. B. Weisspfennig), Algebra-A model theoretic viewpoint, Springer-Verlag (to appear).; R10. Abraham Robinson, (with W. A. J. Luxemburg, co-editor), Contributions to nonstandard analysis, North-Holland, Amsterdam, 1972. MR 476972
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. Royal Soc. Edinburgh Sect. A 61 (1941), 93-101. MR 3, 101. MR 5104
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.: Abraham Robinson, Aerofoil theory of a flat delta wing at supersonic speeds, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2548, 1946/1952. MR 52945
8.: Abraham Robinson, (with T. S. Motzkin), The characterization of algebraic plane curves, Duke Math. J. 14 (1947), 837-853. MR 23556
9.: Abraham Robinson, (with A. D. Young), Note on the application of the linearised theory for compressible flow to transonic speeds, Reports and Memoranda of the Aeronautical Research Council of Great Britain No. 2399, 1947/1951. MR 12, 875. MR 24290
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.: Abraham Robinson, (with S. Kirkby), Interference on a wing due to a body at supersonic speeds, Reports and Memoranda of the Aeronautical Research Council No. 2500, 1947/1952. MR 47472
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.: Abraham Robinson, On some problems of unsteady supersonic aerofoil theory, Proc. Seventh Internat. Congress Appl. Mech. 2 (1948), 500-514. MR 11, 477. MR 33698
14.: Abraham Robinson, On source and vortex distributions in the linearized theory of steady supersonic flow, Quart. J. Mech. Appl. Math. 1 (1948), 408-432. MR 10, 410. MR 28145
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.: Abraham Robinson, On non-associative systems, Proc. Edinburgh Math. Soc. (2) 8 (1949), 111-118. MR 12, 5. MR 35754
18.: Abraham Robinson, On the integration of hyperbolic differential equations, J. London Math. Soc. 25 (1950), 209-217. MR 12, 338. MR 37993
19.: Abraham Robinson, On functional transformations and summability, Proc. London Math. Soc. (2) 52 (1950), 132-160. MR 12, 253. MR 37371
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, pp. 35-51; discussion, pp. 51-52. Centre National de la Recherche Scientifique, Paris, 1953. MR 15, 190. MR 57202
21.: Abraham Robinson, On the application of symbolic logic to algebra, Proc. Internat. Congress of Mathematicians (Cambridge, Mass., 1950), vol. 1, Amer. Math. Soc., Providence, R.I., 1952, pp. 686-694. MR 13, 716. MR 46323
22.: Abraham Robinson, Wave reflexion near a wall, Proc. Cambridge Philos. Soc. 47 (1951), 528-544. MR 12, 875. MR 41630
23.: Abraham Robinson, On axiomatic systems which possess finite models, Methodos (1951), 140-149.
24.: Abraham Robinson, Aerofoil theory for swallow tail wings of small aspect ratio, Aeronaut. Quart. 4 (1952), 69-82. MR 14, 219. MR 49744
25.: Abraham Robinson, L'application de la logique formelle aux mathématiques. Applications scientifiques de la logique mathématique (Actes du 2e Colloque International de Logique Mathématique, Paris, 1952), pp. 51-63; discussion, p. 64; Gauthier-Villars, Paris; E. Nauwelaerts, Louvain, 1954; MR 16, 782. MR 67824
26.: Abraham Robinson, Non-uniform supersonic flow, Quart. Appl. Math. 10 (1953), 307-319. MR 14, 511. MR 51657
27.: Abraham Robinson, Flow around compound lifting units, Sympos. on High Speed Aerodynamics, Ottawa, Canada, (1953), pp. 26-29.
28.: Abraham Robinson, (with G. G. Lorentz), Core-consistence and total inclusion for methods of summability, Canad. J. Math. 6 (1953), 27-34. MR 60041
29.: Abraham Robinson, On some problems of unsteady aerofoil theory, Proc. Second Canad. Sympos. on Aerodynamics (Toronto, 1954), The Inst. of Aerophysics, Univ. of Toronto, Toronto, 1954, pp. 106-122. MR 17, 310. MR 72607
30.: Abraham Robinson, On predicates in algebraically closed fields, J. Symbolic Logic 19 (1954), 103-114. MR 15, 925. MR 62090
31.: Abraham Robinson, Note on an embedding theorem for algebraic systems, J. London Math. Soc. 30 (1955), 249-252. MR 17, 449. MR 73549
32.: Abraham Robinson, (with L. L. Campbell), Mixed problems for hyperbolic partial differential equations, Proc. London Math. Soc. 5 (1955), 129-147. MR 70017
33.: Abraham Robinson, (with P. Gilmore), Metamathematical considerations on the relative irreducibility of polynomials, Canad. J. Math. 7 (1955), 483-489. MR 72088
34.: Abraham Robinson, On ordered fields and definite functions, Math. Ann. 130 (1955), 257-271. MR 17, 822. MR 75932
35.: Abraham Robinson, Further remarks on ordered fields and definite functions, Math. Ann. 130 (1956), 405-409. MR 17, 1180. MR 78352
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 17, 1172. MR 78307
37.: Abraham Robinson, Note on a problem of L. Henkin, J. Symbolic Logic 21 (1956), 33-35. MR 17, 817. MR 75896
38.: Abraham Robinson, Ordered structures and related concepts, Mathematical interpretation of formal systems, North-Holland, Amsterdam, 1955, pp. 51-56. MR 17, 700. MR 75153
39.: Abraham Robinson, Completeness and persistence in the theory of models, Z. Math. Logik Grundlagen Math. 2 (1956), 15-26. MR 17, 1173. MR 78313
40.: Abraham Robinson, Solution of a problem by Erdös-Gillman-Henriksen, Proc. Amer. Math. Soc. 7 (1956), 908-909. MR 18, 374. MR 81265
41.: Abraham Robinson, On the motion of small particles in a potential field of flow, Comm. Pure Appl. Math. 9 (1956), 69-84. MR 17, 1147. MR 78115
42.: Abraham Robinson, Wave propagation in a heterogeneous elastic medium, J. Math. Phys. 36 (1957), 210-222. MR 19, 906. MR 91040
43.: Abraham Robinson, Transient stresses in beams of variable characteristics, Quart. J. Mech. Appl. Math. 10 (1957), 148-159. MR 19, 906. MR 91041
44.: Abraham Robinson, Some problems of definability in the lower predicate calculus, Fund. Math. 44 (1957), 309-329. MR 19, 1032. MR 91922
45.: Abraham Robinson, (with A. H. Lightstone), Syntactical transforms, Trans. Amer. Math. Soc. 86 (1957), 220-245. MR 91246
46.: Abraham Robinson, (with A. H. Lightstone), On the representation of Herbrand functions in algebraically closed fields, J. Symbolic Logic 22 (1957), 187-204. MR 98093
47.: Abraham Robinson, Relative model-completeness and the elimination of quantifiers, Dialectica 12 (1958), 394-407. MR 21 #1265. MR 102472
48.: Abraham Robinson, Outline of an introduction to mathematical logic. I, II, III, Canad. Math. Bull. 1 (1958), 41-54, 113-127, 193-208. MR 20 #5123, #5124; 21 #6321. MR 98668
49.: Abraham Robinson, Outline of an introduction to mathematical logic. IV, Canad. Math. Bull. 2 (1959), 33-42. MR 21 #6321. MR 107596
50.: Abraham Robinson, Solution of a problem of Tarski, Fund. Math. 47 (1959), 179-204. MR 22 #3690. MR 112841
51.: Abraham Robinson, On the concept of a differentially closed field, Bull. Res. Council Israel Sect. F 8F (1959), 113-128. MR 23 #A2323. MR 125016
52.: Abraham Robinson, Obstructions to arithmetical extension and the theorem of Łoś and Suszko, Nederl. Akad. Wetensch. Proc. Ser. A 62 = Indag. Math. 21 (1959), 489-495. MR 22 #2544. MR 111682
53.: Abraham Robinson, Model theory and non-standard arithmetic, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; PWN, Warsaw, 1961, pp. 265-302. MR 26 #32. MR 142463
54.: Abraham Robinson, Local differential algebra, Trans. Amer. Math. Soc. 97 (1960), 427-456. MR 23 #A148. MR 122815
55.: Abraham Robinson, On the mechanization of the theory of equations, Bull. Res. Council Israel Sect. F 9F (1960), 47-70. MR 26 #4910. MR 147394
56.: Abraham Robinson, (with E. Zakon), Elementary properties of ordered Abelian groups, Trans. Amer. Math. Soc. 96 (1960), 222-236. MR 114855
57.: Abraham Robinson, Recent developments in model theory, Logic, Methodology and Philosophy of Science (Proc. 1960 International Congress), Stanford Univ. Press, Stanford, Calif., 1962, 60-79. MR 29 #4668. MR 167395
58.: Abraham Robinson, On the construction of models, Essays on the foundations of math. (Fraenkel anniversary volume), Magnes Press, Hebrew Univ., Jerusalem, 1961, pp. 207-217. MR 29 #23. MR 162719
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 26 #33. MR 142464
61.: Abraham Robinson, A note embedding problems, Fund. Math. 50 (1961/62), 455-461. MR 25 #2946. MR 139514
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.: Abraham Robinson, A basis for the mechanization of the theory of equations, Computer Programming and Formal Systems, North-Holland, Amsterdam, 1963, pp. 95-99. MR 26 #4911. MR 147395
65.: Abraham Robinson, (with S. Halfin), Local partial differential algebra, Trans. Amer. Math. Soc. 109 (1963), 165-180. MR 153673
66.: Abraham Robinson, On languages which are based on non-standard arithmetic, Nagoya Math. J. 22 (1963), 83-117. MR 27 #3532. MR 153569
67.: Abraham Robinson, On generalized limits and linear functionals, Pacific J. Math. 14 (1964), 263-283. MR 29 #1534. MR 164235
68.: Abraham Robinson, (with C. C. Elgot), Random-access stored-program machines, an approach to programming languages, J. Assoc. Comput. Mach. 11 (1964), 365-399. MR 30 #4400. MR 174193
69.: Abraham Robinson, Between logic and mathematics, I.C.S.U. Review 6 (1964), 218-226.
70.: Abraham Robinson, Formalism 64, Logic, Methodology and Philosophy of Science (Proc. 1964 Internat. Congress), North-Holland, Amsterdam, 1965, pp. 228-246. MR 35 #5281. MR 214431
71.: Abraham Robinson, On the theory of normal families, Acta Philos. Fenn. Fasc. 18 (1965), 159-184 (Nevanlinna anniversary volume). MR 32 #5845. MR 188406
72.: Abraham Robinson, (with A. R. Bernstein), Solution of an invariant subspace problem of K. T. Smith and P. R. Halmos, Pacific J. Math. 16 (1966), 421-431. MR 33 #1724. MR 193504
73.: Abraham Robinson, A new approach to the theory of algebraic numbers. I, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 40 (1966), 222-225. MR 35 #5305. MR 214455
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. MR 35 #5306. MR 214456
75.: Abraham Robinson, Topics in non-Archimedean mathematics, Theory of Models (Proc. 1963 Internat. Sympos., Berkeley), North-Holland, Amsterdam, 1965, pp. 285-298. MR 33 #5489. MR 197324
76.: Abraham Robinson, Non-standard theory of Dedekind rings, Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29 (1967), 444-453. MR 36 #6399. MR 223351
77.: Abraham Robinson, Nonstandard arithmetic, Invited address, Bull. Amer. Math. Soc. 73 (1967), 818-843. MR 36 #1319. MR 218231
78.: Abraham Robinson, On some applications of model theory to algebra and analysis, Rend. Mat. 25 (1967), 1-31. MR 219406
79.: Abraham Robinson, (with C. C. Elgot and J. D. Rutledge), Multiple control computer models, Systems and Computer Science, (Proc. Conf., London, Ontario, 1965), Univ. Toronto Press, 1967, pp. 60-76. MR 38 #4073. MR 235770
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; also in book form: Logic and foundations of mathematics (dedicated to A. Heyting on his 70th birthday), Wolters-Noordhoff, Groningen, 1968. MR 37 #21; 40 #1255. MR 224422
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 42 #3054. MR 268155
84.: Abraham Robinson, (with 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 39 #1319. MR 239965
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 38 #4723. MR 236427
86.: Abraham Robinson, Problems and methods of model theory, Aspects of Math. Logic (C.I.M.E., Verenna, 1968), Edizioni Cremonese, Rome, 1969, pp. 181-266. MR 41 #5208. MR 260584
87.: Abraham Robinson, Elementary embeddings of fields of power series, J. Number Theory 2 (1970), 237-247. MR 41 #3451. MR 258805
88.: Abraham Robinson, (with Jon Barwise), Completing theories by forcing, Ann. Math. Logic 2 (1970), 119-142. MR 272613
89.: Abraham Robinson, Compactification of groups and rings and nonstandard analysis, J. Symbolic Logic 34 (1969), 576-588. MR 44 #1765. MR 284540
90.: Abraham Robinson, Forcing in model theory, Symposia Mathematica, Vol. 5 (INDAM, Rome, 1969/70), Academic Press, London, 1971, pp. 69-82. MR 43 #4651. MR 278925
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, Studies in Logic and the Foundations of Mathematics, vol. 63 (Proc. Second Scandinavian Logic Sympos., Oslo, 1970), North-Holland, Amsterdam, 1971, pp. 317-340. MR 50 #9574. MR 357106
93.: Abraham Robinson, Forcing in model theory, Proc. Internat. Congress of Mathematicians, vol. 1, (Nice, 1970), Gauthier-Villars, Paris, 1971, pp. 245-250. MR 505456
94.: Abraham Robinson, On the notion of algebraic closedness for noncommutative groups and fields, J. Symbolic Logic 36 (1971), 441-444. MR 45 #43. MR 290949
95.: Abraham Robinson, Algebraic function fields and nonstandard arithmetic, Contributions to Nonstandard Analysis, North-Holland, Amsterdam, 1972, pp. 1-14. MR 480522
96.: Abraham Robinson, (with E. R. Fisher), Inductive theories and their forcing companions, Israel J. Math. 12 (1972), 95-107. MR 47 #3163. MR 314612
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), part II, 87-109. MR 48 #8464. MR 330126
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 (Hausdorff memorial volume), V.E.B. Deutsch. Verlag Wissensch., Berlin, 1972, pp. 427-433. MR 49 #4980. MR 340225
101.: Abraham Robinson, On bounds in the theory of polynomial ideals, Selected Questions of Algebra and Logic (Mal'cev memorial volume), "Nauka" Sibirsk. Otdel., Novosibirsk, 1973, pp. 245-252. (Russian) MR 49 #2364. MR 337595
102.: Abraham Robinson, Ordered differential fields, J. Combinatorial Theory Ser. A. 14 (1973), 324-333. MR 48 #2124. MR 323768
103.: Abraham Robinson, Nonstandard points on algebraic curves, J. Number Theory 5 (1973), 301-327. MR 396581
104.: Abraham Robinson, Metamathematical problems, J. Symbolic Logic 38 (1973), 500-516. MR 49 #2240. MR 337471
105.: Abraham Robinson, A note on topological model theory, (Dedicated to A. Mostowski on his 60th birthday), Fund. Math. 81 (1973/74), 159-171. MR 49 #7135. MR 342389
106.: Abraham Robinson, Standard and nonstandard number systems, Nieuw Arch. Wisk. (3) 21 (1973), 113-133. MR 434803
107.: Abraham Robinson, A decision method for elementary algebra and geometry-revisited, Proc. Tarski Sympos. (Proc. Sympos. Pure Math., vol.25), Univ. of Calif., Berkeley, Calif., 1971, Amer. Math. Soc., Providence, R. I., 1974, pp. 139-152. MR 51 #2902. MR 366655
108.: Abraham Robinson, Nonstandard arithmetic and generic arithmetic, Proc. Fourth Internat. Congress for Logic, Methodology and Philosophy of Science (P. Suppes et al, editors), North-Holland, Amsterdam, 1973, pp. 137-154. MR 446966
109.: Abraham Robinson, Enlarged sheaves, Victoria Symposium on Nonstandard Analysis (1972), Lecture Notes in Math., vol. 369, Springer-Verlag, Berlin and New York, 1974, pp. 249-260. MR 480013
110.: Abraham Robinson, (with D. J. Brown), The cores of large standard exchange economies, J. Economic Theory (to appear). MR 475731
111.: Abraham Robinson, (with D. J. Brown), Nonstandard exchange economies, Econometrica 43 (1975), 41-55. MR 443867
112.: Abraham Robinson, Concerning progress in the philosophy of mathematics, Proc. Logic Colloquium (Bristol, 1973), (H. E. Rose and J. C. Shepherdson, editors), North-Holland, Amsterdam; American Elsevier, New York, 1975, pp. 41-52. MR 51 #10015. MR 392492
113.: Abraham Robinson, (with P. Roquette), On the finiteness theorem of Siegel and Mahler concerning Diophantine equations, J. Number Theory 7 (1975), 121-176. MR 51 #10222. MR 374022
114.: Abraham Robinson, On constrained denotation, Russell Sympos. Duke Univ.
115.: Abraham Robinson, Algorithms in algebra, Model Theory and Algebra (Saracino and Weispfenning, editors), Lecture Notes in Math., vol. 498, Springer-Verlag, Berlin and New York, 1975. MR 387042
116.: Abraham Robinson, (Written up by G. Takeuti from a draft of an appendix to 115.); Y. A. Young et. al., Obituary, J. London Math. Soc. (to appear).; A. E. Artin, Über die Zerlegung definiter Funktionen in Quadrate, Hamb. Abh. 5 (1927), 100-115.; A-K1. J. Ax and S. Koenen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605-630. MR 32 #2401. MR 184930; A-K2. J. Ax and S. Koenen, Diophantine problems over local fields. II, Amer. J. Math. 87 (1965), 631-648. MR 32 #2402. MR 184931; A-K3. J. Ax and S. Koenen, Diophantine problems over local fields. III, Ann. of Math. (2) 83 (1966), 437-456. MR 34 #1262. MR 201378; B. L. Blum, Generalized algebraic structures, Thesis, M.I.T., 1968.; C. P. J. Cohen, Decision procedures for real and p-adic fields, Comm. Pure Appl. Math. 22 (1969), 131-151. MR 39 #5342. MR 244025; Co. P. M. Cohn, The embedding of firs in skew fields, Proc. London Math. Soc. (3) 23 (1971), 193-213. MR 45 #6866. MR 297814; E-S. P. C. Eklof and G. Sabbagh, Model completions and modules, Ann. Math. Logic 2 (1971), 251-295. MR 277372; E1. Ju. L. Eršov, On elementary theory of maximal normalized fields, Algebra i Logika Sem. 4 (1965), no. 3, 31-70. MR 33 #1307. MR 193086; E2. Ju. L. Eršov, Fields with a solvable theory, Dokl. Akad. Nauk SSSR 174 (1967), 19-20 = Soviet Math. Dokl. 8 (1967), 575-576. MR 35 #5424. MR 214575; G1. K. Gödel, Die Vollständigkeit der Axiome der logischen Funktionenkalküls, Monatsh Math. Phys. 37 (1930), 349-360. MR 1549799; G2. K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I, Monatsh Math. Phys. 38 (1931), 173-198. MR 1549910; G3. K. Gödel, s/b Prefatory remarks to 2 ed., "Non-Standard Analysis (by A. Robinson)", North-Holland, Amsterdam, 1974.; G. G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95 (1926), 736-788. MR 1512302; H. L. Henkin, The completeness of formal systems, Dissertation, Princeton Univ., 1947.; H-W. J. Hirschfeld and W. H. Wheeler, Forcing, arithmetic, division rings, Lecture Notes in Math., vol. 454, Springer-Verlag, Berlin and New York, 1975, p. 454. MR 389581; IJ. Israel J. Math., Robinson memorial volume (to appear).; I. I. Kaplansky, Maximal fields with valuations, Duke Math. J. 9 (1942), 302-321. MR 3, 264. MR 6161; K. S. Kochen, Integer valued rational functions over the p-adic numbers, Number Theory (Proc. Sympos. Pure Math., vol. 12), (Leveque and Straus, editors), Amer. Math. Soc., Providence, R.I., 1969, pp. 57-73. MR 41 #1685. MR 257030; KR. G. Kreisel, Mathematical significance of consistency proofs, J. Symbolic Logic 23 (1958), 155-182. MR 22 #6710. MR 115912; L1. S. Lang, Introduction to algebraic geometry, Interscience, New York and London, 1958. MR 20 #7021. MR 100591; L2. S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1971. (1st ed., 1965; MR 33 #5416). MR 197234; L0. P. 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Additional Information:

DOI: 10.1090/S0002-9904-1977-14334-6
PII: S 0002-9904(1977)14334-6

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