×

zbMATH — the first resource for mathematics

Categoricity in power. (English) Zbl 0151.01101

Keywords:
set theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. Ehrenfeucht, On theories categorical in power, Fund. Math. 44 (1957), 241 – 248. · Zbl 0105.00601
[2] -, Theories having at least continuum many non-isomorphic models in each power, Abstract 550-23, Notices Amer, Math. Soc. 5 (1958), 680-681.
[3] A. Ehrenfeucht and A. Mostowski, Models of axiomatic theories admitting automorphisms, Fund. Math. 43 (1956), 50 – 68. · Zbl 0073.00704
[4] D. Hilbert and P. Bernays, Grundlagen der Mathematik, Vol. 2, Julius Springer, Berlin, 1939. · JFM 65.0021.02
[5] B. Jónsson, Homogeneous universal relational systems, Math. Scand. 8 (1960), 137 – 142. · Zbl 0173.00505
[6] Bjarni Jónsson, Algebraic extensions of relational systems, Math. Scand. 11 (1962), 179 – 205. · Zbl 0201.34403
[7] E. Kamke, Theory of Sets. Translated by Frederick Bagemihl, Dover Publications, Inc., New York, N. Y., 1950. · Zbl 0037.03501
[8] H. Jerome Keisler, Ultraproducts and elementary classes, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 477 – 495. · Zbl 0118.01501
[9] J. Łoś, On the categoricity in power of elementary deductive systems and some related problems, Colloquium Math. 3 (1954), 58 – 62. · Zbl 0055.00505
[10] Michael Morley and Robert Vaught, Homogeneous universal models, Math. Scand. 11 (1962), 37 – 57. · Zbl 0112.00603
[11] A Mostowski and A. Tarski, Boolesche Ringe mit geordneter Basis, Fund. Math. 32 (1939), 69-86. · Zbl 0021.10903
[12] F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. (2) 30 (1929), 291-310. · JFM 55.0032.04
[13] C. Ryll-Nardzewski, On theories categorical in power \( \leqq {\aleph _0}\), Bull. Acad. Polon. Sci. Cl. III 7 (1959), 545-548. · Zbl 0117.01101
[14] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375 – 481. · Zbl 0017.13502
[15] Alfred Tarski and Robert L. Vaught, Arithmetical extensions of relational systems, Compositio Math 13 (1958), 81 – 102. · Zbl 0091.01201
[16] 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. · Zbl 0056.24802
[17] -, Homogeneous universal models of complete theories, Abstract 550-29, Notices Amer. Math. Soc. 5 (1958), 775.
[18] 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.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.