ON THE EXISTENCE OF LARGE ANTICHAINS FOR DEFINABLE QUASI-ORDERS

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 defi...

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Bibliographic Details
Published in:The Journal of symbolic logic 2020-03, Vol.85 (1), p.103-108
Main Authors: D.MILLER, BENJAMIN, VIDNYÁNSZKY, ZOLTÁN
Format: Article
Language:English
Subjects:
Equality
New Testament
Theorems
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Summary: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.
ISSN:0022-4812
1943-5886
DOI:10.1017/jsl.2019.84