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Published June 17, 2016 | Submitted
Journal Article Open

Borel equivalence relations and cardinal algebras

Abstract

We show that Tarski's concept of cardinal algebra appears naturally in the context of the current theory of Borel equivalence relations. As a result one can apply Tarski's theory to discover a number of interesting laws governing the structure of Borel equivalence relations, which, in retrospect rather surprisingly, have not been realized before.

Additional Information

© 2016 Instytut Matematyczny PAN. Received 21 December 2015; revised 20 April 2016; Published online: 17 June 2016. Research partially supported by NSF Grant DMS-1464475. We would like to thank Simon Thomas for his help with Theorem 4.3.

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