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KEISLER’S ORDER IS NOT LINEAR, ASSUMING A SUPERCOMPACT

Published online by Cambridge University Press:  01 August 2018

DOUGLAS ULRICH
DOUGLAS ULRICH*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF MARYLAND COLLEGE PARK, MD 20742, USAE-mail:ds_ulrich@hotmail.com
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Abstract

We show that if there is a supercompact cardinal, then Keisler’s order is not linear. More specifically, let Tn,k be the theory of the generic n-clique free k-ary graph for any n > k ≥ 3, and let TCas be the simple nonlow theory described by Casanovas in [2]. Then we show that TCas$$Tn,k always, and if there is a supercompact cardinal then Tn,k$$TCas.

Keywords

03C55uncountable model theoryKeisler’s orderultraproducts
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 634 - 641
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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