Submission date: 11 April 2023

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 afterforcing base monotonicity can or can not satisfy extension (on arbitrary sets). This study is based onthe results of Chernikov, Ramsey, Dobrowolski and Granger.

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Full text arXiv 2304.05404: pdf, ps.