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Events for day: Wednesday 23 December 2020    
           16:00 - 18:00     Mathtematical Logic Weekly Seminar
The Herwig--Lascar Property of Groups, Ultraextensive Structures and Vershik's Conjecture

School
MATHEMATICS

We study a notion of HL-extension (HL standing for Herwig--Lascar) for a structure in a finite relational language $mathcal{L}$. We give a description of all finite minimal HL-extensions of a given finite $mathcal{L}$-structure. In addition, we study a group-theoretic property considered by Herwig--Lascar and show that it is closed under taking free products. We also introduce notions of coherent extensions and ultraextensive $mathcal{L}$-structures and show that every countable $mathcal{L}$-structure can be extended to a countable ultraextensive structure. Finally, we introduce a notion of omnigenous group and verify a conjecture of Versh ...