Invariant Universality for Projective Planes

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the author from [13] to show that these equivalence relations are invari...

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Bibliographic Details
Published inReports on mathematical logic Vol. 58; no. 58; pp. 15 - 27
Main Author Paolini, Gianluca
Format Journal Article
LanguageEnglish
Published Kraków Wydawnictwo Uniwersytetu Jagiellońskiego 01.01.2023
Jagiellonian University Press
Jagiellonian University-Jagiellonian University Press
Subjects
Economy
Equivalence
Set theory
in variant universality
descriptive set theory
projective planes
biembeddability relation
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Summary:We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the author from [13] to show that these equivalence relations are invariantly universal, in the sense of [3], and thus in particular complete analytic. We also introduce a new kind of Borel reducibility relation for standard Borel G-spaces, which requires the preservation of stabilizers, and explain its connection with the notion of full embeddings commonly considered in category theory.
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ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.23.002.18801