On the Boolean algebras of definable sets in weakly o‐minimal theories

Mathematical Logic Quarterly 50 (3):241-248 (2004)

Abstract
We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within expansions of Boolean lattices, every weakly o-minimal theory is p-ω-categorical
Keywords Weakly o‐minimal theory  p‐ω‐categorical theory  Boolean algebra  linear order
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DOI 10.1002/malq.200310095
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