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2008•Proceedings of the American Mathematical SocietyOpen access

Morasses and finite support iterations

Bernhard Irrgang

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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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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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Available 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.

Key concepts: Forcing (mathematics), Construct (python library), Mathematics, Omega, Chain (unit), Kappa, Pure mathematics, Applied mathematics

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