The interior operator logic and product topologies
HTML articles powered by AMS MathViewer
- by Joseph Sgro
- Trans. Amer. Math. Soc. 258 (1980), 99-112
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554321-4
- PDF | Request permission
Abstract:
In this paper we present a model theory of the interior operator on product topologies with continuous functions. The main results are a completeness theorem, an axiomatization of topological groups, and a proof of an interpolation and definability theorem.References
- K. Bruce, Ideal models and not so ideal problems (to appear).
C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
- Helen F. Cullen, Introduction to general topology, D. C. Heath and Company, Boston, Mass., 1968. MR 0221455
- Leon Henkin, The completeness of the first-order functional calculus, J. Symbolic Logic 14 (1949), 159–166. MR 33781, DOI 10.2307/2267044
- Leon Henkin, A generalization of the concept of $\omega$-consistency, J. Symbolic Logic 19 (1954), 183–196. MR 63324, DOI 10.2307/2268617 E. Hewitt and K. Ross, Abstract harmonic analysis, Academic Press, New York, 1963.
- Carol R. Karp, Languages with expressions of infinite length, North-Holland Publishing Co., Amsterdam, 1964. MR 0176910
- H. Jerome Keisler, Logic with the quantifier “there exist uncountably many”, Ann. Math. Logic 1 (1970), 1–93. MR 263616, DOI 10.1016/S0003-4843(70)80005-5
- J. A. Makowsky and S. Shelah, The theorems of Beth and Craig in abstract model theory. I. The abstract setting, Trans. Amer. Math. Soc. 256 (1979), 215–239. MR 546916, DOI 10.1090/S0002-9947-1979-0546916-0
- A. Mostowski, On a generalization of quantifiers, Fund. Math. 44 (1957), 12–36. MR 89816, DOI 10.4064/fm-44-1-12-36
- Abraham Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland Publishing Co., Amsterdam, 1963. MR 0153570
- Joseph Sgro, Completeness theorems for topological models, Ann. Math. Logic 11 (1977), no. 2, 173–193. MR 462913, DOI 10.1016/0003-4843(77)90016-X
- Joseph Sgro, Completeness theorems for topological models, Ann. Math. Logic 11 (1977), no. 2, 173–193. MR 462913, DOI 10.1016/0003-4843(77)90016-X —, Decision problems for topological abelian groups (in preparation).
- Joseph Sgro, Maximal logics, Proc. Amer. Math. Soc. 63 (1977), no. 2, 291–298. MR 491143, DOI 10.1090/S0002-9939-1977-0491143-2 —, An application of topological model theory to Chang’s model logic, J. Symbolic Logic (to appear).
- Joseph Sgro, Completeness theorems for continuous functions and product topologies, Israel J. Math. 25 (1976), no. 3-4, 249–272. MR 539984, DOI 10.1007/BF02757004
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 258 (1980), 99-112
- MSC: Primary 03C80
- DOI: https://doi.org/10.1090/S0002-9947-1980-0554321-4
- MathSciNet review: 554321