Invariant Universality for Projective Planes
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RIS BIB ENDNOTEInvariant Universality for Projective Planes
Publication date: 12.2023
Reports on Mathematical Logic, 2023, Number 58, pp. 15-27
https://doi.org/10.4467/20842589RM.23.002.18801Authors
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 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.
A previous version of this paper has appeared on the ArXiv with co-author F. Calderoni. The author and F. Calderoni have agreed that the present paper is presented as G. Paolini as the only author. We thank F. Calderoni for his contributions to the writing of this paper.
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Information: Reports on Mathematical Logic, 2023, Number 58, pp. 15-27
Article type: Original article
Department of Mathematics “Giuseppe Peano”, University of Torino, Italy
Published at: 12.2023
Article status: Open
Licence: CC BY
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English