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ON THE EXISTENCE OF LARGE ANTICHAINS FOR DEFINABLE QUASI-ORDERS

Published online by Cambridge University Press:  10 December 2019

BENJAMIN D. MILLER  and
ZOLTÁN VIDNYÁNSZKY
BENJAMIN D. MILLER
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITÄT WIEN WÄHRINGER STRASSE 25 1090 WIEN AUSTRIAE-mail:benjamin.miller@univie.ac.atURL:http://www.logic.univie.ac.at/~millerb45/
ZOLTÁN VIDNYÁNSZKY
Affiliation:
KURT GÖDEL RESEARCH CENTER FOR MATHEMATICAL LOGIC UNIVERSITÄT WIEN WÄHRINGER STRASSE 25 1090 WIEN AUSTRIAE-mail:zoltan.vidnyanszky@univie.ac.atURL:http://www.logic.univie.ac.at/zoltan.vidnyanszky/
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Abstract

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We simultaneously generalize Silver’s perfect set theorem for co-analytic equivalence relations and Harrington-Marker-Shelah’s Dilworth-style perfect set theorem for Borel quasi-orders, establish the analogous theorem at the next definable cardinal, and give further generalizations under weaker definability conditions.

Keywords

Primary 03E1528A05antichainchaindichotomyDilworthHarrington-Marker-Shelahquasi-ordersmooth

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 1 , March 2020 , pp. 103 - 108
Copyright
Copyright © The Association for Symbolic Logic 2019 

References

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