Let κ be an uncountable cardinal with κ = κ<κ. Given a cardinal μ, we equip the set κμ consisting of all functions from κ to μ with the topology whose basic open sets consist of all extensions of… (More)

Given an uncountable regular cardinal κ, a partial order is κstationarily layered if the collection of regular suborders of P of cardinality less than κ is stationary in Pκ(P). We show that weak… (More)

The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds… (More)

In this paper, we study trees of uncountable regular heights containing ascending paths of small width. This combinatorial property of trees generalizes the concept of a cofinal branch and it causes… (More)

Let L be a finite first-order language and Mn | n < ω be a sequence of finite L-models containing models of arbitrarily large finite car-dinality. If the intersection of less than continuum-many… (More)

We show that there is a class-sized partial order P with the property that forcing with P preserves ZFC, supercompact cardinals, inaccessible cardinals and the value of 2κ for every inaccessible… (More)