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NSOP_1 theories Kim, Byunghan
Description
Let $T$ be an NSOP$_1$ theory. Recently I. Kaplan and N. Ramsey proved that in $T$, the so-called Kim-independence ($\phi(x,a_0)$ Kim-divides over $A$ if there is a Morley sequence $a_i$ such that $\{\phi(x,a_i)\}_i$ is inconsistent) satisfies nice properties over models such as extension, symmetry, and type-amalgamation. In a joint work with J. Dobrowolski and N. Ramey we continue to show that in $T$ with nonforking existence, Kim-independence also satisfies the properties over any sets, in particular, Kimâ s lemma, and 3-amalgamation for Lascar types hold. Modeling theorem for trees in a joint paper with H. Kim and L. Scow plays a key role in showing Kimâ s lemma. If time permits I will talk about a result extending the non-finiteness (except 1) of the number of countable models of supersimple theories to the NSOP$_1$ theory context.
Item Metadata
Title |
NSOP_1 theories
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-10-16T12:31
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Description |
Let $T$ be an NSOP$_1$ theory. Recently I. Kaplan and N. Ramsey proved that in $T$, the so-called Kim-independence ($\phi(x,a_0)$ Kim-divides over $A$ if there is a Morley sequence $a_i$ such that $\{\phi(x,a_i)\}_i$ is inconsistent) satisfies nice properties over models such as extension, symmetry, and type-amalgamation.
In a joint work with J. Dobrowolski and N. Ramey we continue to show that in $T$ with nonforking existence, Kim-independence also satisfies the properties over any sets, in particular, Kimâ s lemma, and 3-amalgamation for Lascar types hold. Modeling theorem for trees in a joint paper with H. Kim and L. Scow plays a key role in showing Kimâ s lemma.
If time permits I will talk about a result extending the non-finiteness (except 1) of the number of countable models of supersimple theories to the NSOP$_1$ theory context.
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Extent |
40.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Yonsei University
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Series | |
Date Available |
2019-04-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0378210
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International