Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
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
MathSciNet review: 0218231
Full-text PDF

References | Additional Information

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

  • 1. James Ax and Simon Kochen, Diophantine problems over local fields. I, Amer. J. Math. 87 (1965), 605–630. MR 0184930 (32 #2401)
  • 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 P. J. Cohen, Decision procedures for real and p-adic fields, Unpublished.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, A. C. Morel, and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962/1963), 195–228. MR 0142459 (26 #28)
  • 5. D. K. Harrison, Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. No. 68 (1966), 62. MR 0207735 (34 #7550)
  • 6. Helmut Hasse, Zur arithmetischen Theorie der algebraischen Funktionenkörper, Jber. Deutsch. Math. Verein 52 (1942), 1–48 (German). MR 0008077 (4,239c)
  • 7. Leon Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949), 159–166. MR 0033781 (11,487d)
  • 8. H. Jerome Keisler, Ultraproducts and elementary classes, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 477–495. MR 0140396 (25 #3816)
  • 9. John G. Kemeny, Undecidable problems of elementary number theory, Math. Ann. 135 (1958), 160–169. MR 0098685 (20 #5140)
  • 10. Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 0138548 (25 #1992)
  • 11. W. Krull, Galoissche Theorie unendlicher algebraischer Erweiterungen, Math. Ann. 100 (1928), 678-698.
  • 12. Serge Lang, Rapport sur la cohomologie des groupes, W. A. Benjamin, Inc., New York-Amsterdam, 1967 (French). MR 0212073 (35 #2948)
  • 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. 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 (27 #2425)
  • 15. 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 (29 #1141)
  • 16. 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 (15,190a)
  • 17. 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 (26 #32)
  • 18. Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854 (34 #5680)
  • 19. A. Robinson, A new approach to the theory of algebraic numbers, Accad. Naz. Lincei Rend. (8) 40 (1966), 222-225, 770-774.
  • 20. Abraham Robinson, Non-standard theory of Dedekind rings, Nederl. Akad. Wetensch. Proc. Ser. A 70=Indag. Math. 29 (1967), 444–452. MR 0223351 (36 #6399)
  • 21. 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 (55 #7767)
  • 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: http://dx.doi.org/10.1090/S0002-9904-1967-11809-3
PII: S 0002-9904(1967)11809-3