COHERENT SYSTEMS OF FINITE SUPPORT ITERATIONS
نویسندگان
چکیده
منابع مشابه
Coherent Systems of Finite Support Iterations
We introduce a forcing technique to construct three-dimensional arrays of generic extensions through FS (finite support) iterations of ccc posets, which we refer to as 3D-coherent systems. We use them to produce models of new constellations in Cichoń’s diagram, in particular, a model where the diagram can be separated into 7 different values. Furthermore, we show that this constellation of 7 va...
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 کاملIterations with Mixed Support
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 کاملSome applications of mixed support iterations
We give some applications of mixed support forcing iterations to the topics of disjoint stationary sequences and internally approachable sets. In the first half of the paper we study the combinatorial content of the idea of a disjoint stationary sequence, including its relation to adding clubs by forcing, the approachability ideal, canonical structure, the proper forcing axiom, and properties r...
متن کاملPreservation theorems for countable support forcing iterations
A major theme of [12] is preservation theorems for iterated forcing. These are theorems of the form “if 〈Pξ : ξ ≤ κ〉 is a countable support forcing iteration based on 〈Q̇ξ : ξ < κ〉 and each Q̇ξ has property such-and-such then Pκ has property thus-and-so.” The archetypal preservation theorem is the Fundamental Theorem of Proper Forcing [12, chapter III], which states that if each Q̇ξ is proper in V...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2018
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2017.20