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A Sacks-like forcing

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#reference-request #set-theory #forcing
266
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Henkin's Model Existence Theorem and Forcing

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#logic #set-theory #model-theory #forcing
18
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Coding a new real using a variant of the Baumgartner forcing

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#forcing
68
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Prove that if $c.c.(\mathbb{P}) < \omega$, then every $G$ that is $\mathbb{P}$-generic over $M$ is also in $M$

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#set-theory #forcing
168
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Kunen problem on forcing $(2^{\aleph_0}=\aleph_2)^{\sf HOD}$ and $\sf L= HOD^{HOD}\subsetneq HOD\subsetneq V$

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#logic #set-theory #forcing
76
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Random forcing does not add Cohen real.

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#logic #forcing
161
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Which forcing axioms may be destroyed through forcings which preserve $2^{\aleph_0}=\aleph_2$?

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#set-theory #forcing
166
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When forcing, do we always have to have a generic filter on the forcing notion in $V$? What happens if we don't have one?

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#set-theory #forcing
144
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Foundations of Forcing in Kunen

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#logic #set-theory #foundations #forcing
61
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Factor lemma for general iterated forcing

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#set-theory #forcing
72
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In Solovay's proof that generic extension is also generic over any intermediate model, why is transfinite induction required?

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#set-theory #forcing
86
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The Factor Lemma in Levy collapse

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#set-theory #forcing
85
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Is Forcing only possible in first-order theories?

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#set-theory #model-theory #forcing
71
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Quotient forcing and intermediate model

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#set-theory #forcing
54
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Definition of Separately Generic Forcing Extensions

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#logic #set-theory #forcing

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