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Notions of relative ubiquity for invariant sets of relational structures

Published online by Cambridge University Press:  12 March 2014

Paul Bankston  and
Wim Ruitenburg
Paul Bankston
Affiliation:
Department of Mathematics, Marquette University, Milwaukee, Wisconsin 53233
Wim Ruitenburg
Affiliation:
Department of Mathematics, Marquette University, Milwaukee, Wisconsin 53233
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Abstract

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers ω as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on ω. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on ω is ubiquitous in the set of linear orderings on ω.

Keywords

Spaces of relational structuresubiquitygamesBaire categoryprobabilitycomplete theories.
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 948 - 986
Copyright
Copyright © Association for Symbolic Logic 1990

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