Models of complete theories
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- by R. L. Vaught PDF
- Bull. Amer. Math. Soc. 69 (1963), 299-313
References
- 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 146080, DOI 10.2140/pjm.1962.12.835
- A. Ehrenfeucht, On theories categorical in power, Fund. Math. 44 (1957), 241–248. MR 96606, DOI 10.4064/fm-44-2-241-248 3. A. Ehrenfeucht, Theories having at least continuum many nonisomorphic models in each infinite power, Notices Amer. Math. Soc. 5 (1958), 680-681.
- A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), 50–68. MR 84456, DOI 10.4064/fm-43-1-50-68
- Erwin Engeler, Äquivalenzklassen von $n$-Tupeln, Z. Math. Logik Grundlagen Math. 5 (1959), 340–345 (German). MR 141598, DOI 10.1002/malq.19590051411
- Erwin Engeler, Unendliche Formeln in der Modelltheorie, Z. Math. Logik Grundlagen Math. 7 (1961), 154–160 (German). MR 151386, DOI 10.1002/malq.19610070711 7. E. Engeler, Ein Reduktionstheorem für unendliche Formeln, Math. Ann. (to appear).
- P. Erdös, L. Gillman, and M. Henriksen, An isomorphism theorem for real-closed fields, Ann. of Math. (2) 61 (1955), 542–554. MR 69161, DOI 10.2307/1969812
- 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
- Gebhard Fuhrken, Bemerkung zu einer Arbeit E. Engelers, Z. Math. Logik Grundlagen Math. 8 (1962), 277–279 (German). MR 146074, DOI 10.1002/malq.19620080308 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.
- Leon Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949), 159–166. MR 33781, DOI 10.2307/2267044
- Bjarni Jónsson, Universal relational systems, Math. Scand. 4 (1956), 193–208. MR 96608, DOI 10.7146/math.scand.a-10468
- B. Jónsson, Homogeneous universal relational systems, Math. Scand. 8 (1960), 137–142. MR 125021, DOI 10.7146/math.scand.a-10601
- 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
- Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 138548, DOI 10.2307/1970235
- J. Łoś, On the categoricity in power of elementary deductive systems and some related problems, Colloq. Math. 3 (1954), 58–62. MR 61561, DOI 10.4064/cm-3-1-58-62 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.
- R. C. Lyndon, Properties preserved under algebraic constructions, Bull. Amer. Math. Soc. 65 (1959), 287–299. MR 111687, DOI 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.
- Michael Morley and Robert Vaught, Homogeneous universal models, Math. Scand. 11 (1962), 37–57. MR 150032, DOI 10.7146/math.scand.a-10648
- 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, Éditions du Centre National de la Recherche Scientifique (CNRS), Paris, 1958, pp. 19–32 (French). MR 0106162
- Rodolfo A. Ricabarra, Conjuntos ordenados y ramificados (Contribución al estudio del problema de Suslin), Universidad Nacional del Sur, Instituto de Matemática, Bahía Blanca, 1958 (Spanish). MR 0117177
- 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, DOI 10.1016/S1385-7258(56)50008-X
- Abraham Robinson, Complete theories, North-Holland Publishing Co., Amsterdam, 1956. MR 0075897 29. C. Ryll-Nardzewski, On theories categorical in power $łeq \aleph _{0}$, Bull. Acad. Polon. Sci., Sér. Math. Astr. Phys. 7 (1959), 545-548.
- Lars Svenonius, $\aleph _{0}$-categoricity in first-order predicate calculus, Theoria (Lund) 25 (1959), 82–94. MR 138539, DOI 10.1111/j.1755-2567.1959.tb00294.x
- Lars Svenonius, $\aleph _{0}$-categoricity in first-order predicate calculus, Theoria (Lund) 25 (1959), 82–94. MR 138539, DOI 10.1111/j.1755-2567.1959.tb00294.x
- Alfred Tarski, A decision method for elementary algebra and geometry, University of California Press, Berkeley-Los Angeles, Calif., 1951. 2nd ed. MR 0044472, DOI 10.1525/9780520348097
- 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
- Alfred Tarski and Robert L. Vaught, Arithmetical extensions of relational systems, Compositio Math. 13 (1958), 81–102. MR 95121
- 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, DOI 10.1016/S1385-7258(54)50058-2
- 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
Additional Information
- Journal: Bull. Amer. Math. Soc. 69 (1963), 299-313
- DOI: https://doi.org/10.1090/S0002-9904-1963-10903-9
- MathSciNet review: 0147396