منابع مشابه
Forcings constructed along morasses
In a previous paper [11], we introduced a way of constructing a forcing along a simplified (κ, 1)-morass such that the forcing satisfies a chain condition. The basic idea is to generalize iterated forcing with finite support as introduced by Solovay and Tennenbaum, which works with continuous, commutative systems of complete embeddings. However, instead of considering a linear system of embeddi...
متن کاملSuperatomic Boolean Algebras Constructed from Morasses
By using the notion of a simplified (n, 1)-morass, we construct n-thin-tall, K-thin-thick and, in a forcing extension, K-very thin-thick superatomic Boolean algebras for every infinite regular cardinal n.
متن کاملMorasses 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.
متن کاملWide Scattered Spaces and Morasses
We show that it is relatively consistent with ZFC that 2ω is arbitrarily large and every sequence s = 〈sα : α < ω2〉 of infinite cardinals with sα ≤ 2ω is the cardinal sequence of some locally compact scattered space.
متن کاملHigher-dimensional Forcing
We present a method of constructing ccc forcings: Suppose first that a continuous, commutative system of complete embeddings between countable forcings indexed along ω1 is given. Then its direct limit satisfies ccc by a well-known theorem on finite support iterations. However, this limit has size at most ω1. To get larger forcings, we do not consider linear systems but higher-dimensional system...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2011
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1318338841