Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Nonstandard arithmetic


Author: Abraham Robinson
Journal: Bull. Amer. Math. Soc. 73 (1967), 818-843
DOI: https://doi.org/10.1090/S0002-9904-1967-11809-3
MathSciNet review: 0218231
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. J. Ax and S. Kochen, Diophantine problems over local fields, Amer. J. Math.87 (1965), 605-630, 631-698. MR 184930
  • 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 P. J. Cohen, Decision procedures for real and p-adic fields, Unpublished.
  • 4. T. Frayne, D. C. Morel and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962), 195-227. MR 142459
  • 5. D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. No. 68 (1966). MR 207735
  • 6. H. Hasse, Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper, Teil I, Klassenkörpertheorie, Jber. Deutsch. Math.- Verein. 35 (1926), 1-66; 36 (1927), 233-311. MR 8077
  • 7. L. Henkin, The completeness of the first order functional calculus, J. Symbolic Logic 14 (1949), 159-166. MR 33781
  • 8. H. J. Keisler, Ultraproducts and elementary classes, Proc. Roy. Acad. Sci. Amsterdam Ser. A 64 (1962), 477-495. MR 140396
  • 9. J. G. Kemeny, Undecidable problems of elementary number theory, Math. Ann.135 (1958), 160-169. MR 98685
  • 10. S. Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 79 (1961), 221-261. MR 138548
  • 11. W. Krull, Galoissche Theorie unendlicher algebraischer Erweiterungen, Math. Ann. 100 (1928), 678-698.
  • 12. S. Lang, Rapport sur la cohomologie des groupes, Benjamin, New York, 1966. MR 212073
  • 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).
  • 14. R. MacDowell and E. Specker, Modelle der Arithmetik, Infinitistic Methods (Symposium on Foundations of Mathematics, Warsaw, 1959), Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 257-263. MR 152447
  • 15. E. Mendelson, On non-standard models for number theory, Essays on the Foundations of Mathematics (Fraenkel anniversary volume), Magnes Press, Jerusalem, 1961, pp. 259-268. MR 163842
  • 16. A. Robinson, Les rapports entre le calcul déductif et l'interprétation sémantique d'un système axiomatique, Colloques Internationaux du Centre National de la Recherche Scientifique, No. 36, Paris, 1953, pp. 35-52. MR 57202
  • 17. A. Robinson, Model theory and non-standard arithmetic, Infinitistic Methods (Symposium on Foundations of Mathematics, Warsaw, 1959), Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 265-302. MR 142463
  • 18. A. Robinson, Non-standard analysis, Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1966. MR 205854
  • 19. A. Robinson, A new approach to the theory of algebraic numbers, Accad. Naz. Lincei Rend. (8) 40 (1966), 222-225, 770-774.
  • 20. A. Robinson, Non-standard theory of Dedekind rings, Proc. Roy. Acad. Sci., Amsterdam, (to appear). MR 223351
  • 21. A. Robinson, Non-standard algebraic number theory, Symposium on Applications of Model Theory to Analysis and Algebra, Pasadena, May 1967, (to appear). 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

DOI: https://doi.org/10.1090/S0002-9904-1967-11809-3

American Mathematical Society