Morasses and finite support iterations

Irrgang, Bernhard

doi:10.1090/S0002-9939-08-09525-7

Morasses and finite support iterations
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by Bernhard Irrgang PDF

Proc. Amer. Math. Soc. 137 (2009), 1103-1113 Request permission

Abstract:

We introduce a method of constructing a forcing along a simplified $(\kappa ,1)$-morass such that the forcing satisfies the $\kappa$-chain condition. Alternatively, this may be seen as a method to thin out a larger forcing to get a chain condition. As an application, we construct a ccc forcing that adds an $\omega _2$-Suslin tree. Related methods are Shelah’s historic forcing and Todorcevic’s $\rho$-functions.

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