Garcia, D, Macpherson, D and Steinhorn, C (2015) Pseudofinite structures and simplicity. Journal of Mathematical Logic, 15 (1). 1550002. ISSN 0219-0613
Abstract
We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao’s Algebraic Regularity Lemma is noted.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced electronic version of an article published in Journal of Mathematical Logic, 15, 1, 1550002 (2015) [41 pages] DOI: 10.1142/S0219061315500026. © 2015 World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/jml. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Model theory; finite and pseudofinite structures; dimension; independence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Sep 2015 12:22 |
Last Modified: | 23 Jun 2016 00:34 |
Published Version: | http://dx.doi.org/10.1142/S0219061315500026 |
Status: | Published |
Publisher: | World Scientific Publishing |
Identification Number: | 10.1142/S0219061315500026 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:89861 |