Infinite Time Decidable Equivalence Relation Theory

Notre Dame Journal of Formal Logic 52 (2):203-228 (2011)

Authors
Joel David Hamkins
Oxford University
Abstract
We introduce an analogue of the theory of Borel equivalence relations in which we study equivalence relations that are decidable by an infinite time Turing machine. The Borel reductions are replaced by the more general class of infinite time computable functions. Many basic aspects of the classical theory remain intact, with the added bonus that it becomes sensible to study some special equivalence relations whose complexity is beyond Borel or even analytic. We also introduce an infinite time generalization of the countable Borel equivalence relations, a key subclass of the Borel equivalence relations, and again show that several key properties carry over to the larger class. Lastly, we collect together several results from the literature regarding Borel reducibility which apply also to absolutely $\Delta^1_2$ reductions, and hence to the infinite time computable reductions
Keywords set theory   descriptive set theory   infinite time computation   equivalence relations
Categories (categorize this paper)
DOI 10.1215/00294527-1306199
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,607
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

The Higher Infinite.Akihiro Kanamori - 2000 - Studia Logica 65 (3):443-446.
A Simple Maximality Principle.Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):527-550.
Martin’s Conjecture and Strong Ergodicity.Simon Thomas - 2009 - Archive for Mathematical Logic 48 (8):749-759.
Turing Computable Embeddings.Julia Knight, Sara Miller & M. Vanden Boom - 2007 - Journal of Symbolic Logic 72 (3):901-918.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Actions of Non-Compact and Non-Locally Compact Polish Groups.Sławomir Solecki - 2000 - Journal of Symbolic Logic 65 (4):1881-1894.
Diagonal Actions and Borel Equivalence Relations.Longyun Ding & Su Gao - 2006 - Journal of Symbolic Logic 71 (4):1081 - 1096.
Maximal R.E. Equivalence Relations.Jeffrey S. Carroll - 1990 - Journal of Symbolic Logic 55 (3):1048-1058.
On Σ1 1 Equivalence Relations with Borel Classes of Bounded Rank.Ramez L. Sami - 1984 - Journal of Symbolic Logic 49 (4):1273 - 1283.
? 0 N -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351-358.
Classifying Positive Equivalence Relations.Claudio Bernardi & Andrea Sorbi - 1983 - Journal of Symbolic Logic 48 (3):529-538.
On the Space-Time Ontology of Physical Theories.Kenneth L. Manders - 1982 - Philosophy of Science 49 (4):575-590.
Property Τ and Countable Borel Equivalence Relations.Simon Thomas - 2007 - Journal of Mathematical Logic 7 (1):1-34.
Countable Borel Equivalence Relations.S. Jackson, A. S. Kechris & A. Louveau - 2002 - Journal of Mathematical Logic 2 (01):1-80.
$\Sum_{0}^{N}$ -Equivalence Relations.Andrea Sorbi - 1982 - Studia Logica 41 (4):351 - 358.
Logic Semantics with the Potential Infinite.Theodore Hailperin - 2010 - History and Philosophy of Logic 31 (2):145-159.

Analytics

Added to PP index
2011-04-29

Total views
30 ( #253,591 of 2,325,498 )

Recent downloads (6 months)
9 ( #140,837 of 2,325,498 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature