Forcing continuous epsilon-chains with finite side conditions (Set Theory and Infinity)

Abstract

We introduce a poset that generically adds a continuously increasing epsilon-chain of a length the least uncountable cardinal. This poset is similar to a poset that consists of finite conditions and generically adds a closed cofinal subset of the least uncountable cardinal. As an application, we consider a poset for the Strong Reflection Principle of S. Todorcevic along this line.