CLASS FORCING, THE FORCING THEOREM AND BOOLEAN COMPLETIONS
نویسندگان
چکیده
منابع مشابه
Class forcing, the forcing Theorem and Boolean Completions
The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a condition in the relevant generic filter. We show that both the definability (and, in fact, even the amenability) of the forcing relation and the truth lemma ca...
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This introduction to forcing is based on Chapters 5–6 in T. J. Jech’s book The Axiom of Choice and is written primarily for the Fraenkel-Mostowski Models reading group. Forcing is introduced via Boolean-valued models and generic extensions, and these techniques are used to prove the independence of the axiom of choice of ZF. This is then related back to the theory of FM models. Please inform me...
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The class forcing theorem, which asserts that every class forcing notion P admits a forcing relation P, that is, a relation satisfying the forcing relation recursion—it follows that statements true in the corresponding forcing extensions are forced and forced statements are true—is equivalent over Gödel-Bernays set theory GBC to the principle of elementary transfinite recursion ETROrd for class...
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In this paper we develop the notion of \stratiied" class forcing and show that this property both implies coonality-preservation and is preserved by iterations with the appropriate support. Many Easton-style and Jensen-style forcings are stratiied, as are some more exotic forcings obtained by mixing these types together (see Easton 70], section 36 of Jech 78], Beller-Jensen-Welch 82], Friedman ...
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In the context of proliferation of many logical systems in the area of mathematical logic and computer science, we present a generalization of forcing in institution-independent model theory which is used to prove an abstract Omitting Types Theorem (OTT). We instantiate this general result to many first-order logics, which are, roughly speaking, logics whose sentences can be constructed from at...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2016
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2016.4