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

Daniel Turetsky

Department of Mathematics

Victoria University of Wellington

New Zealand

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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