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$Add(\omega, 1)$ forces $Add(\omega_1$, 1) to not be countably closed.

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#set-theory #forcing
176
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Prove that $\Vdash_{Coll(\omega_1, \kappa)} \Diamond$ where $\kappa$ is the cardinal $2^{\aleph_0}$

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#set-theory #forcing
162
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Partial order which forces finite intersections with sets not in an ultrafilter

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#set-theory #forcing
70
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Incomparable Cardinal Invariants of the Continuum

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#set-theory #descriptive-set-theory #forcing
161
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A model without a choice function

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#set-theory #axiom-of-choice #forcing
54
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Laver forcing, trees and stems

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#set-theory #trees #forcing
128
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A more classical construction of the Feferman Levy model (without symmetric models)

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#set-theory #axiom-of-choice #forcing
49
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A step in the construction of the Solovay model (showing that the Boolean algebra of Borel mod meager sets is complete)

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#set-theory #boolean-algebra #forcing
176
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Model with weakened perfect set property

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#set-theory #axiom-of-choice #forcing
56
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Proof verification: The Cohen algebra of Borel modulo meagre sets is complete.

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#general-topology #set-theory #boolean-algebra #descriptive-set-theory #forcing
52
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Why are there functions in $M[G]$ that are not in $M$?

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#set-theory #forcing
69
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Why can we find certain conditions in a tree forcing $PT_{f,g}$ in the book 'Set theory - on the structure of the real line' by Bartoszynski and Judah

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#set-theory #forcing
183
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Jech's usage of direct / inverse limits in the support of iterated forcing

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#set-theory #limits-colimits #forcing
116
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Countably closed forcing doesn't add new functions whose domain is the natural numbers

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#set-theory #forcing
87
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Is it the property "be unbounded" upwards absulote?

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#set-theory #cardinals #infinity #forcing

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