Delta-Categoricity of Equivalence Structures

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New Zealand Journal of Mathematics

Vol. 39, (2009), Pages 143-149


Asher M. Kach

Department of Mathematics

University of Connecticut

Storrs, Connecticut

United States of America

mailto:asher.kach@uconn.edu

Daniel Turetsky

Department of Mathematics

Victoria University of Wellington

New Zealand

mailto:dan.turetsky@msor.vuw.ac.nz




Abstract We exhibit computable equivalence structures, one \Delta^0_2-categorical and one not \Delta^0_2-categorical, having unbounded character, infinitely many infinite equivalence classes, and no s1-function. This offers a natural example where \Delta^0_2-categoricity and relative \Delta^0_2-categoricity differ.

Keywords equivalence structure, categoricity, relative categoricity.

Classification (MSC2000) Primary: 03C57.

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