منابع مشابه
Morasses and Finite Support Iterations
We introduce a method of constructing a forcing along a simplified (κ, 1)-morass such that the forcing satisfies the κ-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 ω2-Suslin tree. Related methods are Shelah’s historic forcing and Todorcevic’s ρ-functions.
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In this talk we will consider three properties of iterations with mixed (finite/countable) supports: iterations of arbitrary length preserve ω1, iterations of length ≤ ω2 over a model of CH have the א2-chain condition and iterations of length < ω2 over a model of CH do not increase the size of the continuum. Definition 1. Let Pκ be an iterated forcing construction of length κ, with iterands 〈Q̇α...
متن کاملCountable support iterations and large continuum
We prove that any countable support iteration formed with posets with ω2-p.i.c. has ω2-c.c., assuming CH in the ground model. This improves earlier results of Shelah by removing the restriction on the length of the iteration. Thus, we solve the problem of obtaining a large continuum via such forcing iterations.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09525-7