Document Type

Article

Language

eng

Format of Original

10 p.

Publication Date

6-1984

Publisher

Association for Symbolic Logic

Source Publication

Journal of Symbolic Logic

Source ISSN

0022-4812

Original Item ID

DOI: 10.2307/2274179

Abstract

A first order representation (f.o.r.) in topology is an assignment of finitary relational structures of the same type to topological spaces in such a way that homeomorphic spaces get sent to isomorphic structures. We first define the notions "one f.o.r. is at least as expressive as another relative to a class of spaces" and "one class of spaces is definable in another relative to an f.o.r.", and prove some general statements. Following this we compare some well-known classes of spaces and first order representations. A principal result is that if X and Y are two Tichonov spaces whose posets of zero-sets are elementarily equivalent then their respective rings of bounded continuous real-valued functions satisfy the same positive universal sentences. The proof of this uses the technique of constructing ultraproducts as direct limits of products in a category theoretic setting.

Comments

Published version. The Journal of Symbolic Logic, Vol. 49, No. 2 (June 1984): 478-487. DOI. © 1984 The Association for Symbolic Logic. Used with permission.

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