Question

In forcing, would a generic extension $M[G]$ also extend sentences satisfiable by $M$ that are not provable in ZF?

score 55 · Answer 1 · 2022-09-16 17:56:08

55

Views

In forcing, would a generic extension $M[G]$ also extend sentences satisfiable by $M$ that are not provable in ZF?

Published on 16 Sep 2022 - 17:56

score 152 · Answer 2 · 2022-09-27 23:46:08

152

Views

Applying Martin's Axiom to Families of functions

Published on 27 Sep 2022 - 23:46

score 59 · Answer 3 · 2022-10-22 19:04:52

59

Views

If $X \in V[G]$, then $X \cap V \in V[G]$?

Published on 22 Oct 2022 - 19:04

score 51 · Answer 4 · 2022-10-23 12:15:53

51

Views

shooting a club: the complement of a stationary subset becomes non-stationary

Published on 23 Oct 2022 - 12:15

score 73 · Answer 5 · 2022-11-10 17:42:42

73

Views

Forcing problem. Find a subset of a set in the extension which is uncountable according to ground model.

Published on 10 Nov 2022 - 17:42

score 62 · Answer 6 · 2022-11-28 15:57:39

62

Views

Is it consistent for a Dedekind-infinite set $A$ to satisfy the strict inequality $2^{|A|}<2^{\aleph_0}$?

Published on 28 Nov 2022 - 15:57

score 273 · Answer 7 · 2022-12-09 17:46:28

273

Views

Unforceable statements in ZFC

Published on 09 Dec 2022 - 17:46

score 77 · Answer 8 · 2022-12-19 03:22:23

77

Views

Under GCH, the countable support product of Prikry Silver forcing is $\omega_2$-cc

Published on 19 Dec 2022 - 3:22

score 61 · Answer 9 · 2022-12-20 10:34:52

61

Views

An $\aleph_2$-cc forcing which is not proper but doesn't collapse $\omega_1$

Published on 20 Dec 2022 - 10:34

score 152 · Answer 10 · 2022-12-30 00:03:26

152

Views

Why is $\sf MM^{++}$ the strongest forcing axiom?

Published on 30 Dec 2022 - 0:03

score 42 · Answer 11 · 2023-01-03 16:35:18

42

Views

Question about Silver forcing theorem proof

Published on 03 Jan 2023 - 16:35

score 54 · Answer 12 · 2023-01-09 04:43:29

54

Views

Question on iterated forcing from Halbeisen's book.

Published on 09 Jan 2023 - 4:43

score 88 · Answer 13 · 2023-01-16 21:00:41

88

Views

Precise definition of iterated forcing

Published on 16 Jan 2023 - 21:00

score 120 · Answer 14 · 2023-01-19 14:48:30

120

Views

the strength of the axiom of choice used in forcing

Published on 19 Jan 2023 - 14:48

List Question

In forcing, would a generic extension $M[G]$ also extend sentences satisfiable by $M$ that are not provable in ZF?

Applying Martin's Axiom to Families of functions

If $X \in V[G]$, then $X \cap V \in V[G]$?

shooting a club: the complement of a stationary subset becomes non-stationary

Forcing problem. Find a subset of a set in the extension which is uncountable according to ground model.

Is it consistent for a Dedekind-infinite set $A$ to satisfy the strict inequality $2^{|A|}<2^{\aleph_0}$?

Unforceable statements in ZFC

Under GCH, the countable support product of Prikry Silver forcing is $\omega_2$-cc

An $\aleph_2$-cc forcing which is not proper but doesn't collapse $\omega_1$

Why is $\sf MM^{++}$ the strongest forcing axiom?

Question about Silver forcing theorem proof

Question on iterated forcing from Halbeisen's book.

Precise definition of iterated forcing

the strength of the axiom of choice used in forcing

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