The interior operator logic and product topologies

Author:
Joseph Sgro

Journal:
Trans. Amer. Math. Soc. **258** (1980), 99-112

MSC:
Primary 03C80

MathSciNet review:
554321

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**1.**K. Bruce,*Ideal models and not so ideal problems*(to appear).**[1]**C. C. Chang and H. J. Keisler,*Model theory*, North-Holland, Amsterdam, 1973.**[2]**Helen F. Cullen,*Introduction to general topology*, D. C. Heath and Co., Boston, Mass., 1968. MR**0221455****[3]**Leon Henkin,*The completeness of the first-order functional calculus*, J. Symbolic Logic**14**(1949), 159–166. MR**0033781****[4]**Leon Henkin,*A generalization of the concept of 𝜔-consistency*, J. Symbolic Logic**19**(1954), 183–196. MR**0063324****[5]**E. Hewitt and K. Ross,*Abstract harmonic analysis*, Academic Press, New York, 1963.**[6]**Carol R. Karp,*Languages with expressions of infinite length*, North–Holland Publishing Co., Amsterdam, 1964. MR**0176910****[7]**H. Jerome Keisler,*Logic with the quantifier “there exist uncountably many”*, Ann. Math. Logic**1**(1970), 1–93. MR**0263616****[8]**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**, 10.1090/S0002-9947-1979-0546916-0**[9]**A. Mostowski,*On a generalization of quantifiers*, Fund. Math.**44**(1957), 12–36. MR**0089816****[10]**Abraham Robinson,*Introduction to model theory and to the metamathematics of algebra*, North-Holland Publishing Co., Amsterdam, 1963. MR**0153570****[11]**Joseph Sgro,*Completeness theorems for topological models*, Ann. Math. Logic**11**(1977), no. 2, 173–193. MR**0462913****[12]**Joseph Sgro,*Completeness theorems for topological models*, Ann. Math. Logic**11**(1977), no. 2, 173–193. MR**0462913****[13]**-,*Decision problems for topological abelian groups*(in preparation).**[14]**Joseph Sgro,*Maximal logics*, Proc. Amer. Math. Soc.**63**(1977), no. 2, 291–298. MR**0491143**, 10.1090/S0002-9939-1977-0491143-2**[15]**-,*An application of topological model theory to Chang's model logic*, J. Symbolic Logic (to appear).**[16]**Joseph Sgro,*Completeness theorems for continuous functions and product topologies*, Israel J. Math.**25**(1976), no. 3-4, 249–272. MR**0539984**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
03C80

Retrieve articles in all journals with MSC: 03C80

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1980-0554321-4

Article copyright:
© Copyright 1980
American Mathematical Society