slideshow 3

Seminar on Reckoning

On countably saturated linear orders and graphs

Ziemowit Kostana
IM CAS

 

Seminar on Reckoning
Wednesday, 31. July 2019 - 11:00 to 15:00

Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building

A linear order L is countably saturated if for any countable subsets A,B of L, such that any element of A is less than any element of B, we can find an element of L between them. This obvious generalization of density corresponds to ``countable saturation” from model theory. We’ll say, that a countably saturated linear order L is prime, if every countably saturated linear order contains an isomorphic copy of L.
I’d like to present a characterization of the prime countably saturated linear order and say something about related results concerning certain classes of uncountable graphs. I will present more or less detailed proofs, depending on time.