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

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

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References found in this work

Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
p-ℵ0-Categorical Lattice-Ordered Structures.Carlo Toffalori - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):23-28.
On pseudo -n0-categorical theories.Annalisa Marcja & Carlo Toffalori - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (35):533-540.
The Boolean spectrum of an $o$-minimal theory.Charles Steinhorn & Carlo Toffalori - 1989 - Notre Dame Journal of Formal Logic 30 (2):197-206.

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