A Caltech Library Service

Higher-dimensional obstructions for star reductions

Kruckman, Alex and Panagiotopoulos, Aristotelis (2021) Higher-dimensional obstructions for star reductions. Fundamenta Mathematicae, 255 (2). pp. 209-230. ISSN 0016-2736. doi:10.4064/fm35-2-2021.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


A ∗-reduction between two equivalence relations is a Baire measurable reduction which preserves generic notions, i.e., preimages of meager sets are meager. We show that a ∗-reduction between orbit equivalence relations induces generically an embedding between the associated Becker graphs. We introduce a notion of dimension for Polish G-spaces which is generically preserved under ∗-reductions. For every natural number n we define a free action of S_∞ whose dimension is n on every invariant Baire measurable non-meager set. We also show that the S_∞-space which induces the equivalence relation =+ of countable sets of reals is ∞-dimensional on every invariant Baire measurable non-meager set. We conclude that the orbit equivalence relations associated to all these actions are pairwise incomparable with respect to ∗-reductions.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Panagiotopoulos, Aristotelis0000-0002-7695-4842
Additional Information:© 2021 IMPAN. Published online: 20 April 2021. This work greatly benefited from a visit of Alex Kruckman at the California Institute of Technology in the Spring 2018. The authors gratefully acknowledge the hospitality and the financial support of the Institute.
Funding AgencyGrant Number
Subject Keywords:Polish group, Polish space, Borel reduction, Baire measurable, ∗-reduction, category preserving, isomorphism, n-amalgamation
Issue or Number:2
Classification Code:2000 Mathematics Subject Classification. Primary 03E15; Secondary 54H05.
Record Number:CaltechAUTHORS:20211008-183537226
Persistent URL:
Official Citation:Higher-dimensional obstructions for star reductions Alex Kruckman, Aristotelis Panagiotopoulos Fundamenta Mathematicae 255 (2021), 209-230
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111292
Deposited By: George Porter
Deposited On:08 Oct 2021 19:44
Last Modified:08 Oct 2021 19:44

Repository Staff Only: item control page