Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)



On the complexity of the relations of isomorphism and bi-embeddability

Author: Luca Motto Ros
Journal: Proc. Amer. Math. Soc. 140 (2012), 309-323
MSC (2010): Primary 03E15
Published electronically: May 16, 2011
MathSciNet review: 2833542
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Given an $ \mathcal{L}_{\omega_1\omega}$-elementary class $ \mathcal{C}$, that is, the collection of the countable models of some $ \mathcal{L}_{\omega_1 \omega}$-sentence, denote by $ \cong_{\mathcal{C}}$ and $ \equiv_{\mathcal{C}}$ the analytic equivalence relations of, respectively, isomorphisms and bi-embeddability on $ \mathcal{C}$. Generalizing some questions of A. Louveau and C. Rosendal, in a paper by S. Friedman and L. Motto  Ros they proposed the problem of determining which pairs of analytic equivalence relations $ (E,F)$ can be realized (up to Borel bireducibility) as pairs of the form $ (\cong_{\mathcal{C}}, \equiv_{\mathcal{C}})$, $ \mathcal{C}$ some $ \mathcal{L}_{\omega_1\omega}$-elementary class (together with a partial answer for some specific cases). Here we will provide an almost complete solution to such a problem: under very mild conditions on $ E$ and $ F$, it is always possible to find such an $ \mathcal{L}_{\omega_1\omega}$-elementary class $ \mathcal{C}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E15

Retrieve articles in all journals with MSC (2010): 03E15

Additional Information

Luca Motto Ros
Affiliation: Mathematisches Institut–Abteilung für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, Eckerstraße, 1, D-79104 Freiburg im Breisgau, Germany

Keywords: Analytic equivalence relation, isomorphism, (bi-)embeddability, Borel reducibility.
Received by editor(s): April 15, 2010
Received by editor(s) in revised form: November 10, 2010
Published electronically: May 16, 2011
Additional Notes: The author would like to thank the FWF (Austrian Research Fund) for generously supporting this research through project number P 19898-N18.
Communicated by: Julia Knight
Article copyright: © Copyright 2011 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia