Friday 29 March 2024 |
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 ... |