Saharon Shelah
Published 2005-10-11, updated 2019-01-28Version 3
We mainly investigate model of set theory with restricted choice, e.g., ZF + DC + "the family of countable subsets of lambda is well ordered for every lambda" (really local version for a given lambda). In this frame much of pcf theory can be generalized. E.g., there is a class of regular cardinals, and we can prove cardinal inequality.
On the sequence $\langle \text{pcf}^α(A): α\in \text{Ord} \rangle$
Souslin trees at successors of regular cardinals
The Future of Set Theory
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