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Tuesday, 5 March 2024 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Rob Sullivan, Universität Münster<br />
Title: Generic embeddings into Fraïssé structures
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Abstract <br />
<p>This project, in the writing-up stage, is work with A. Codenotti (Münster), A. Panagiotopoulos (Vienna) and J.Winkel.</p><p><br></p><p>Let M be a Fraïssé structure, and let A be a countably infinite structure which is embeddable in M. If M has free amalgamation, then there exists a Katetov embedding of A into M: an embedding such that each automorphism of A extends to an automorphism of M. Is this embedding "common" or "uncommon"?</p><p><br></p><p>To answer this, we investigate generic embeddings of A into M. An embedding of A into M is said to be generic if it lies in a comeagre set inside the Polish space Emb(A, M).</p><p><br></p><p>We will answer the following three questions:</p><p><br></p><p>- When are two embeddings of A into M generically isomorphic via an automorphism of M?</p><p><br></p><p>- When is A generically corigid (i.e. Aut(M/A) trivial)?</p><p><br></p><p>- Let g lie in Aut(A). When is g generically extensible to an automorphism of M?</p><p><br></p><p>We will also provide a wide range of examples in the context of these three questions.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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