On some Fraisse limits with free amalgamation

Abstract

In the first part of this work the notion of stable Kim-forking is discussed and some context on this matter is given. In the second part a general way of building some examples of NSOP1 theories as the limit of some Fraisse class satisfying stronger conditions is given. These limits will satisfy existence, that Kim-independence coincide with algebraic independence, and that forking independence is obtained by forcing base monotonicity on Kim-forking over arbitrary sets. These theories also come with a stationary independence relation. This study is based on the results of Baudisch, Ramsey, Chernikov and Kruckman.