Submission date: 12 March 2024

Abstract:

In the first section of this work we discuss some curiosities around stable Kim-forking. In the second section we give a general way of building some known and some new examples of NSOP1 theories as the limit of some Fraisse class satisfying some strong conditions. These limits will satisfy existence, that Kim independence and algebraic independence coincide over arbitrary sets, that forcing base monotonicity on Kim-independance gives forking independence, and they come with a stationary independence relation. This study is based on the results of Baudish, Ramsey, Chernikov and Kruckman.

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Full text arXiv 2403.07616: pdf, ps.