UNCOUNTABLE TREES AND COHEN -REALS
نویسندگان
چکیده
منابع مشابه
Small Forcings and Cohen Reals
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The following is our main result. Theorem 1.1 Suppose that A ⊆ ω1 and = [A]. Then there exists a cardinal preserving generic extension [x] of the ground universe by a generic real x such that (i) A ∈ [x] – this implies [x] = [x], and A ∈ Δ 1 (x) in [x], (ii) x is a minimal real over , that is, x ∈ , and if a set Y belongs to [x], then x ∈ [Y ] or Y ∈ , 1) (iii) there is a club C ∈ [x], C ⊆ ω1, ...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2019
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2019.46