Louise Hay Logic Seminar
David Gonzalez
Berkeley
Scott Sentence Complexities of Linear Orderings
Abstract: Abstract: The concept of Scott sentence complexity was introduced by Alvir, Greenberg, Harrison-Trainor and Turetsky and gives a way of assigning countable structures to elements of the Borel hierarchy. By calculating the Scott sentence complexities occurring in a class of structures we obtain a detailed picture of the descriptive complexity of its isomorphism relation. We study possible Scott sentence complexities of linear orderings using two approaches. First, we investigate the effect of the Friedman-Stanley embedding on Scott sentence complexity and show that it only preserves complexities. We then take a more direct approach and exhibit linear orderings of all Scott sentence complexities except and for a limit ordinal. We show that the former can not be the Scott sentence complexity of a linear ordering. In the process we develop new techniques which appear to be helpful to calculate the Scott sentence complexities of structures in general.
This talk is based on joint work with Dino Rossegger.
Thursday November 9, 2023 at 4:00 PM in 427 SEO