A note on some example of NSOP1 theories
Yvon Bossut (ICJ, AGL)
TL;DR
This paper explores various examples of NSOP1 theories, examining Kim-forking behavior and its properties, including extension and base monotonicity, building on recent foundational results.
Contribution
It provides new and known examples of NSOP1 theories and analyzes Kim-forking properties, highlighting nuanced behaviors in these theories.
Findings
Kim-forking can or cannot satisfy extension in NSOP1 theories.
Behavior of Kim-forking after forcing base monotonicity varies.
Examples illustrate complex Kim-forking phenomena in NSOP1 theories.
Abstract
We present here some known and some new examples of non-simple NSOP1 theories and some behaviour that Kim-forking can exhibit in these theories, in particular that Kim-forking after forcing base monotonicity can or can not satisfy extension (on arbitrary sets). This study is based on the results of Chernikov, Ramsey, Dobrowolski and Granger.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Limits and Structures in Graph Theory