Extension, Translation, and the Cantor-Bernstein Property

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Abstract

The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.

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Author Profiles

Thomas William Barrett
University of California at Santa Barbara
Hans Halvorson
Princeton University

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