Invariantly universal analytic quasi-orders
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- by Riccardo Camerlo, Alberto Marcone and Luca Motto Ros PDF
- Trans. Amer. Math. Soc. 365 (2013), 1901-1931 Request permission
Abstract:
We introduce the notion of an invariantly universal pair $(S,E)$ where $S$ is an analytic quasi-order and $E\subseteq S$ is an analytic equivalence relation. This means that for any analytic quasi-order $R$ there is a Borel set $B$ invariant under $E$ such that $R$ is Borel bireducible with the restriction of $S$ to $B$. We prove a general result giving a sufficient condition for invariant universality, and we demonstrate several applications of this theorem by showing that the phenomenon of invariant universality is widespread. In fact it occurs for a great number of complete analytic quasi-orders, arising in different areas of mathematics, when they are paired with natural equivalence relations.References
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Additional Information
- Riccardo Camerlo
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
- MR Author ID: 663257
- Email: camerlo@calvino.polito.it
- Alberto Marcone
- Affiliation: Dipartimento di Matematica e Informatica, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy
- Email: alberto.marcone@dimi.uniud.it
- Luca Motto Ros
- Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Vienna, Austria
- Address at time of publication: Albert-Ludwigs-Universität Freiburg, Mathematisches Institut – Abteilung für Mathematische Logik, Eckerstraße, 1, D-79104 Freiburg im Breisgau, Germany
- MR Author ID: 865960
- Email: luca.motto.ros@math.uni-freiburg.de
- Received by editor(s): March 25, 2010
- Received by editor(s) in revised form: May 2, 2011
- Published electronically: October 11, 2012
- Additional Notes: The first author’s research was partially supported by FWF (Austrian Research Fund) through Project number P 19898-N18. The third author’s research was supported by FWF through Project number P 19898-N18. The second author’s research was partially supported by FWF through Project number P 19898-N18 and by PRIN of Italy.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 1901-1931
- MSC (2010): Primary 03E15
- DOI: https://doi.org/10.1090/S0002-9947-2012-05618-2
- MathSciNet review: 3009648