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arXiv:2011.04034 [math.LO]AbstractReferencesReviewsResources

A Strictly $ \text{NSOP}_3 $ Theory

Massoud Pourmahdian, Ali N. Valizadeh

Published 2020-11-08Version 1

We define the new notion of a $ \mu$-uniformly-counter-collapsed structure using which we introduce a theory $ \mathbb{T}_\mu $ serving as the first example of a strictly $ \text{NSOP}_3 $ theory. This answers a question posed in [DS04] and reappeared in [SU08] and [MS16]. The existence of such a theory provides a better understanding of the hierarchy of unstable theories without the strict order property.

Comments: 23 pages
Categories: math.LO
Subjects: 03C45
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