Imaginaries in Boolean algebras

Mathematical Logic Quarterly 58 (3):217-235 (2012)

Abstract

Given an infinite Boolean algebra B, we find a natural class of equation image-definable equivalence relations equation image such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from equation image. It follows that B together with the family of sorts determined by equation image admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean algebras, obtained in 10

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References found in this work

Small Theories of Boolean Ordered o-Minimal Structures.Roman Wencel - 2002 - Journal of Symbolic Logic 67 (4):1385-1390.
Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
Definable Sets in Boolean Ordered o-Minimal Structures. II.Roman Wencel - 2003 - Journal of Symbolic Logic 68 (1):35-51.
Weak Elimination of Imaginaries for Boolean Algebras.Roman Wencel - 2005 - Annals of Pure and Applied Logic 132 (2-3):247-270.

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