Fraenkel–Carnap Questions for Equivalence Relations

  • George Weaver Park Science Center, Bryn Mawr College
  • Irena Penev Department of Mathematics, Columbia University

Abstract

An equivalence is a binary relational system A = (A,ϱA) where ϱA is an equivalence relation on A. A simple expansion of an equivalence is a system of the form (Aa1…an) were A is an equivalence and a1,…,an are members of A. It is shown that the Fraenkel-Carnap question when restricted to the class of equivalences or to the class of simple expansions of equivalences has a positive answer: that the complete second-order theory of such a system is categorical, if it is finitely axiomatizable.

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Author Biographies

George Weaver, Park Science Center, Bryn Mawr College
Irena Penev, Department of Mathematics, Columbia University
Published
2011-05-19
How to Cite
WEAVER, George; PENEV, Irena. Fraenkel–Carnap Questions for Equivalence Relations. The Australasian Journal of Logic, [S.l.], v. 10, may 2011. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1825>. Date accessed: 23 jan. 2020. doi: https://doi.org/10.26686/ajl.v10i0.1825.