Nonstandard arithmetic
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- Bull. Amer. Math. Soc. 73 (1967), 818-843
References
- James Ax and Simon Kochen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605–630. MR 184930, DOI 10.2307/2373065 2. C. Chevalley, Généralisation de la théorie du corps de classes pour les extensions infinies, J. Math. Pures Appl. (9) 15 (1936), 359-371. 3. P. J. Cohen, Decision procedures for real and p-adic fields, Unpublished.
- T. Frayne, A. C. Morel, and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962/63), 195–228. MR 142459, DOI 10.4064/fm-51-3-195-228
- D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. 68 (1966), 62. MR 207735
- Helmut Hasse, Zur arithmetischen Theorie der algebraischen Funktionenkörper, Jber. Deutsch. Math.-Verein. 52 (1942), 1–48 (German). MR 8077
- Leon Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949), 159–166. MR 33781, DOI 10.2307/2267044
- H. Jerome Keisler, Ultraproducts and elementary classes, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 477–495. MR 0140396, DOI 10.1016/S1385-7258(61)50048-0
- John G. Kemeny, Undecidable problems of elementary number theory, Math. Ann. 135 (1958), 160–169. MR 98685, DOI 10.1007/BF01343100
- Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 138548, DOI 10.2307/1970235 11. W. Krull, Galoissche Theorie unendlicher algebraischer Erweiterungen, Math. Ann. 100 (1928), 678-698.
- Serge Lang, Rapport sur la cohomologie des groupes, W. A. Benjamin, Inc., New York-Amsterdam, 1967 (French). MR 0212073 13. W. A. J. Luxemburg, A new approach to the theory of monads, Symposium on Applications of Model Theory to Analysis and Algebra, Pasadena, May 1967, (to appear).
- R. Mac Dowell and E. Specker, Modelle der Arithmetik, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 257–263 (German). MR 0152447
- Elliott Mendelson, On non-standard models for number theory, Essays on the foundations of mathematics, Magnes Press, Hebrew Univ., Jerusalem, 1961, pp. 259–268. MR 0163842
- 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, vol. 1950, Centre National de la Recherche Scientifique, Paris, 1953, pp. 35–51; discussion, pp. 51–52 (French). MR 0057202
- 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
- Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854 19. A. Robinson, A new approach to the theory of algebraic numbers, Accad. Naz. Lincei Rend. (8) 40 (1966), 222-225, 770-774.
- Abraham Robinson, Non-standard theory of Dedekind rings, Nederl. Akad. Wetensch. Proc. Ser. A 70=Indag. Math. 29 (1967), 444–452. MR 0223351, DOI 10.1016/S1385-7258(67)50062-8
- 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 434803 22. J.-P. Serre, Cohomologie Galoisienne, Lecture Notes in Mathematics No. 5, Springer, Berlin, 1964. 23. T. Skolem, Über die Nichtcharakterisierbarkeit der Zahlenreihe mittels endlich oder unendlich vieler Aussagen mit ausschliesslich Zahlenvariablen, Fund. Math.23 (1934), 150-161.
Additional Information
- Journal: Bull. Amer. Math. Soc. 73 (1967), 818-843
- DOI: https://doi.org/10.1090/S0002-9904-1967-11809-3
- MathSciNet review: 0218231