#### 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.

#### Recommended Citation

Bankston, Paul, "Expressive Power in First Order Topology" (1984). *Mathematics, Statistics and Computer Science Faculty Research and Publications*. 131.

https://epublications.marquette.edu/mscs_fac/131

## 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.