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Borel equivalence relations and cardinal algebras

Macdonald, Henry L. and Kechris, Alexander S. (2016) Borel equivalence relations and cardinal algebras. Fundamenta Mathematicae, 235 . pp. 183-198. ISSN 0016-2736. doi:10.4064/fm242-4-2016.

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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.

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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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Subject Keywords:countable Borel equivalence relation, Borel reducibility, cardinal algebra
Classification Code:MSC: Primary 03E15; Secondary 28A05, 54H05
Record Number:CaltechAUTHORS:20161130-102008360
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72439
Deposited By: Tony Diaz
Deposited On:30 Nov 2016 19:32
Last Modified:11 Nov 2021 05:01

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