Ioannis Souldatos: L_{omega_1,omega}-sentences with maximal models in two cardinalities

Thursday, February 9, 2017, from 4 to 5:30pm
East Hall, room 2866

Speaker: Ioannis Souldatos (University of Detroit Mercy)

Title: L_{omega_1,omega}-sentences with maximal models in two cardinalities

Abstract:

In this talk, we will present some examples on complete L_{omega_1,omega}-sentences with maximal models in (at least) two cardinalities.

Sample theorems:

Theorem: There is a complete L_{omega_1,omega}-sentence that characterizes aleph_2 and has maximal models in aleph_1 and aleph_2.

Theorem: Assume 2^{aleph_0}>aleph_n. Then there is a complete L_{omega_1,omega}-sentence with maximal models in cardinalities 2^{aleph_0}, 2^{aleph_1},…,2^{aleph_n}.

The main construction behind these theorems is a refinement of a construction of J. Knight. This is recent work of J. Baldwin and the speaker.

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