KEISLER’S ORDER IS NOT LINEAR, ASSUMING A SUPERCOMPACT

Author:

ULRICH DOUGLAS

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference11 articles.

1. Realization of φ-types and Keisler’s order

2. A dividing line within simple unstable theories

3. [1] Buechler S. , Lascar strong types in some simple theories, this Journal, vol. 64 (1999), no. 2, pp. 817–824.

4. The number of types in simple theories

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1. Some simple theories from a Boolean algebra point of view;Annals of Pure and Applied Logic;2024-01

2. Keisler's order is not simple (and simple theories may not be either);Advances in Mathematics;2021-12

3. An example of a new simple theory;Trends in Set Theory;2020

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