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

Thursday, February 16, 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, part II

Abstract:

This will be part II of the talk on complete L_{omega_1,omega}-sentences with maximal models
in (at least) two cardinalities. The talk will be self-contained.

Sample theorems

Theorem: If kappa is homogeneously characterizable and mu is the least such that 2^mu>=kappa, then there is a complete L_{omega_1,omega}-sentence with maximal models in cardinalities
2^lambda, for all mu<=lambdaaleph_0 is the least such that mu^omega>=kappa, then there is a complete L_{omega_1,omega}-sentence with maximal models in cardinalities kappa^omega and kappa.

Theorem (Baldwin-Shelah) If mu is the first measurable cardinal and phi belongs to L_{omega_1,omega}, then no model of phi of size greater or equal to mu is maximal with respect to the L_{omega_1,omega}-elementary substructure relation.

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