$\mathbb{1}\Vdash S\subset\kappa$ and $\not\exists\beta<\kappa$ such that $\mathbb{1}\Vdash S\subset\beta$, contradicts $\mathbb{1}\Vdash |S|<\kappa$.

score 253 · Answer 10 · 2016-10-26 13:58:31

253

Views

Rasiowa-Sikorski Lemma

Published on 26 Oct 2016 - 13:58

score 143 · Answer 11 · 2016-10-30 05:02:44

143

Views

$PFA \implies SOCA$. (Or using forcing to prove theorems unrelated to consistency.)

Published on 30 Oct 2016 - 5:02

score 111 · Answer 12 · 2016-10-31 03:14:49

111

Views

Countably closed posets don't add a new uncountable W-free set. (Or $\kappa$-Aronszajn trees remain $\kappa$-Aronszajn.)

Published on 31 Oct 2016 - 3:14

score 196 · Answer 13 · 2016-11-26 20:38:17

196

Views

"Partial" Levy Collapse mantaining $\kappa$ inaccessible. (Solovay model.)

Published on 26 Nov 2016 - 20:38

score 229 · Answer 14 · 2016-12-02 17:39:25

229

Views

Does adding $\kappa$ Cohen reals preserve a Suslin tree?

Published on 02 Dec 2016 - 17:39

score 83 · Answer 15 · 2016-12-19 22:25:47

83

Views

Masters condition and factorization of forcings

Published on 19 Dec 2016 - 22:25

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$\mathbb{1}\Vdash S\subset\kappa$ and $\not\exists\beta<\kappa$ such that $\mathbb{1}\Vdash S\subset\beta$, contradicts $\mathbb{1}\Vdash |S|<\kappa$.

Rasiowa-Sikorski Lemma

$PFA \implies SOCA$. (Or using forcing to prove theorems unrelated to consistency.)

Countably closed posets don't add a new uncountable W-free set. (Or $\kappa$-Aronszajn trees remain $\kappa$-Aronszajn.)

"Partial" Levy Collapse mantaining $\kappa$ inaccessible. (Solovay model.)

Does adding $\kappa$ Cohen reals preserve a Suslin tree?

Masters condition and factorization of forcings

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