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)

 

Models of complete theories


Author: R. L. Vaught
Journal: Bull. Amer. Math. Soc. 69 (1963), 299-313
MathSciNet review: 0147396
Full-text PDF

References | Additional Information

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

  • 1. C. C. Chang and H. Jerome Keisler, Applications of ultraproducts of pairs of cardinals to the theory of models, Pacific J. Math. 12 (1962), 835–845. MR 0146080 (26 #3606)
  • 2. A. Ehrenfeucht, On theories categorical in power, Fund. Math. 44 (1957), 241–248. MR 0096606 (20 #3089)
  • 3. A. Ehrenfeucht, Theories having at least continuum many nonisomorphic models in each infinite power, Notices Amer. Math. Soc. 5 (1958), 680-681.
  • 4. A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), 50–68. MR 0084456 (18,863a)
  • 5. Erwin Engeler, Äquivalenzklassen von 𝑛-Tupeln, Z. Math. Logik Grundlagen Math. 5 (1959), 340–345 (German). MR 0141598 (25 #4996)
  • 6. Erwin Engeler, Unendliche Formeln in der Modelltheorie, Z. Math. Logik Grundlagen Math. 7 (1961), 154–160 (German). MR 0151386 (27 #1371)
  • 7. E. Engeler, Ein Reduktionstheorem für unendliche Formeln, Math. Ann. (to appear).
  • 8. P. Erdös, L. Gillman, and M. Henriksen, An isomorphism theorem for real-closed fields, Ann. of Math. (2) 61 (1955), 542–554. MR 0069161 (16,993e)
  • 9. T. Frayne, A. C. Morel, and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962/1963), 195–228. MR 0142459 (26 #28)
  • 10. Gebhard Fuhrken, Bemerkung zu einer Arbeit E. Engelers, Z. Math. Logik Grundlagen Math. 8 (1962), 277–279 (German). MR 0146074 (26 #3600)
  • 11. G. Fuhrken, First-order languages with a generalized quantifier. Minimal models of first-order theories, Doctoral dissertation, University of California, Berkeley, Calif., 1962.
  • 12. G. Fuhrken, On minimal models of complete theories, Notices Amer. Math. Soc. 9 (1962), 146. On generalized quantifiers, Ibid. p. 132. A Skolem-type normal form for languages with a generalized quantifier, Ibid., pp. 320-321.
  • 13. G. Fuhrken and R. Vaught, Non-characterizability of the ordering of the natural numbers, Notices Amer. Math. Soc. 9 (1962), 321.
  • 14. Leon Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949), 159–166. MR 0033781 (11,487d)
  • 15. Bjarni Jónsson, Universal relational systems, Math. Scand. 4 (1956), 193–208. MR 0096608 (20 #3091)
  • 16. B. Jónsson, Homogeneous universal relational systems, Math. Scand. 8 (1960), 137–142. MR 0125021 (23 #A2328)
  • 17. H. Jerome Keisler, Ultraproducts and elementary classes, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 477–495. MR 0140396 (25 #3816)
  • 18. Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 0138548 (25 #1992)
  • 19. J. Łoś, On the categoricity in power of elementary deductive systems and some related problems, Colloquium Math. 3 (1954), 58–62. MR 0061561 (15,845c)
  • 20. J. Łoś, Quelques remarques, théorèmes, et problèmes sur les classes définissables d'algèbres, Mathematical Interpretation of Formal Systems, pp. 98-113, North Holland Publ. Co., Amsterdam, 1955.
  • 21. R. C. Lyndon, Properties preserved under algebraic constructions, Bull. Amer. Math. Soc. 65 (1959), 287–299. MR 0111687 (22 #2549), http://dx.doi.org/10.1090/S0002-9904-1959-10321-9
  • 22. M. Morley, Categoricity in power, Notices Amer. Math. Soc. 9 (1962) 218.
  • 23. M. Morley, Categoricity in power, Doctoral dissertation, University of Chicago, Chicago, Ill., 1962.
  • 24. Michael Morley and Robert Vaught, Homogeneous universal models, Math. Scand. 11 (1962), 37–57. MR 0150032 (27 #37)
  • 25. Andrzej Mostowski, Quelques observations sur l’usage des méthodes non finitistes dans la méta-mathématique, Le raisonnement en mathématiques et en sciences expérimentales, Colloques Internationaux du Centre National de la Recherche Scientifique, LXX, Editions du Centre National de la Recherche Scientifique, Paris, 1958, pp. 19–32 (French). MR 0106162 (21 #4896)
  • 26. Rodolfo A. Ricabarra, Conjuntos ordenados y ramificados (Contribución al estudio del problema de Suslin), Instituto de Matematica, Universidad Nacional del Sur, Bahía Blanca, 1958 (Spanish). MR 0117177 (22 #7960)
  • 27. 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 0078307 (17,1172d)
  • 28. Abraham Robinson, Complete theories, North-Holland Publishing Co., Amsterdam, 1956. MR 0075897 (17,817b)
  • 29. C. Ryll-Nardzewski, On theories categorical in power $łeq \aleph \sb{0}$, Bull. Acad. Polon. Sci., Sér. Math. Astr. Phys. 7 (1959), 545-548.
  • 30. Lars Svenonius, ℵ₀-categoricity in first-order predicate calculus, Theoria (Lund) 25 (1959), 82–94. MR 0138539 (25 #1986a)
  • 31. Lars Svenonius, On minimal models of first-order systems, Theoria (Lund) 26 (1960), 44–52. MR 0138541 (25 #1986c)
  • 32. Alfred Tarski, A decision method for elementary algebra and geometry, University of California Press, Berkeley and Los Angeles, Calif., 1951. 2nd ed. MR 0044472 (13,423a)
  • 33. Alfred Tarski, Some notions and methods on the borderline of algebra and metamathematics, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 1, Amer. Math. Soc., Providence, R. I., 1952, pp. 705–720. MR 0045068 (13,521b)
  • 34. Alfred Tarski and Robert L. Vaught, Arithmetical extensions of relational systems, Compositio Math 13 (1958), 81–102. MR 0095121 (20 #1627)
  • 35. Robert L. Vaught, Applications to the Löwenheim-Skolem-Tarski theorem to problems of completeness and decidability, Nederl. Akad. Wetensch. Proc. Ser. A. 57 = Indagationes Math. 16 (1954), 467–472. MR 0063993 (16,208c)
  • 36. R. L. Vaught, Denumerable models of complete theories, Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Pergamon, Oxford; Państwowe Wydawnictwo Naukowe, Warsaw, 1961, pp. 303–321. MR 0186552 (32 #4011)


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1963-10903-9
PII: S 0002-9904(1963)10903-9