Cardinal Characteristics of Models of Set Theory

2018/11/13 by Ulrich, Douglas
#03C55 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1811.05444

Abstract

We continue our investigation =of Shelah's interpretability orders \trianglelefteq^*_κ as well as the new orders \trianglelefteq^×_κ. In particular, we give streamlined proofs of the existence of minimal unstable, unsimple and nonlow theories in these orders, and we give a similar analysis of the hypergraph examples T_{n, k} of Hrushovski. We also prove that if B is a complete Boolean algebra with the λ-c.c., then no nonprincipal ultrafilter on U λ⁺-saturates any unsimple theory.

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