Document Type

Article

Language

eng

Format of Original

12 p.

Publication Date

7-2011

Publisher

Springer

Source Publication

Archive for Mathematical Logic

Source ISSN

0933-5846

Original Item ID

doi: 10.1007/s00153-011-0230-2

Abstract

The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is unchanged when we move among the lattice bases of a compactum. In this paper we define syntactically the expansive sentences, and show each of them to be base free. We also show that many well-known properties of compacta may be expressed using expansive sentences; and that any property so expressible is closed under inverse limits and co-existential images. As a byproduct, we conclude that co-existential images of pseudo-arcs are pseudo-arcs. This is of interest because the corresponding statement for confluent maps is still open, and co-existential maps are often—but not always—confluent.

Comments

Accepted version. Archive for Mathematical Logic, Vol. 50, No. 5/6 (July, 2011): 531-542. DOI. © 2011 Springer. Used with permission.

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