Phd records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 18:56:27 +0000Aspects of Definability for Equivalence Relations
https://resolver.caltech.edu/CaltechTHESIS:05312017-155530848
Authors: {'items': [{'email': 'wcchan.caltech@gmail.com', 'id': 'Chan-William', 'name': {'family': 'Chan', 'given': 'William'}, 'orcid': '0000-0002-0661-1764', 'show_email': 'NO'}]}
Year: 2017
DOI: 10.7907/Z90P0X3M
<p>This thesis will show that in the constructible universe L and set forcing extensions of L, there are no almost Borel reductions of the well-ordering equivalence relation into the admissibility equivalence relation and no Borel reductions of the isomorphism relation of any counterexample to Vaught's conjecture into the admissibility equivalence relation.</p>
<p>Let E be an analytic equivalence relation on a Polish space X with all classes Borel. Let I be a sigma-ideal on X such that its associated forcing of I-positive Borel subsets is a proper forcing. Assuming sharps of appropriate sets exist, it will be shown that there is an I-positive Borel subset of X on which the restriction of E is a Borel equivalence relation.</p>
<p>Assuming there are infinitely many Woodin cardinals below a measurable cardinal, then for any equivalence relation E in L(R) with all Borel classes and sigma-ideal I whose associated forcing is proper, there is an I-positive Borel set on which the restriction of E is Borel.</p>https://thesis.library.caltech.edu/id/eprint/10236