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Abraham Robinson, 1918-1974


Author: Angus J. Macintyre
Journal: Bull. Amer. Math. Soc. 83 (1977), 646-666
DOI: https://doi.org/10.1090/S0002-9904-1977-14334-6
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. 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. Kurt Gödel, Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatsh. Math. Phys. 37 (1930), no. 1, 349–360 (German). MR 1549799, https://doi.org/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, https://doi.org/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, https://doi.org/10.1007/BF01206635
    Handbook of mathematical logic, Studies in Logic and the Foundations of Mathematics, vol. 90, North-Holland Publishing Co., Amsterdam, 1977. With the cooperation of H. J. Keisler, K. Kunen, Y. N. Moschovakis and A. S. Troelstra. MR 457132
    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


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

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