Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Base-free formulas in the lattice-theoretic study of compacta

Base-free formulas in the lattice-theoretic study of compacta 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Base-free formulas in the lattice-theoretic study of compacta

Bankston, Paul
Archive for Mathematical Logic , Volume 50 (6) – Feb 24, 2011
Download PDF
12 pages

Loading next page...
 
/lp/springer-journals/base-free-formulas-in-the-lattice-theoretic-study-of-compacta-tIUX7rPep5

References (24)

Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer-Verlag
Subject
Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-011-0230-2
Publisher site
See Article on Publisher Site

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.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Feb 24, 2011

There are no references for this article.