Question

Proving that the boolean prime ideal theorem does not hold in a permutation model

score 65 · Answer 1 · 2026-04-13 00:37:10

Proving that the boolean prime ideal theorem does not hold in a permutation model

Published on 13 Apr 2026 - 0:37

score 60 · Answer 2 · 2026-04-14 08:22:22

Counterexample for $\prod_{i<\nu} \kappa_i=(\sup_{i<\nu}\kappa_i)^{\nu}$ when $\kappa_i$ is not an increasing $\nu$-sequence of cardinals

score 439 · Answer 3 · 2026-04-14 02:57:46

439

Views

Models of set theory where not every set can be linearly ordered

Published on 14 Apr 2026 - 2:57

score 418 · Answer 4 · 2026-04-08 18:50:39

418

Views

Motivation of the von Neumann definition of ordinals

Published on 08 Apr 2026 - 18:50

score 138 · Answer 5 · 2026-04-09 18:25:06

138

Views

Is it possible that $\mathcal{X} = \mathcal{Y}$, yet $\mathcal{X} \in \mathcal{Y}$?

Published on 09 Apr 2026 - 18:25

score 48 · Answer 6 · 2026-04-12 22:17:18

48

Views

If $M$ is a transitive set and $R$ well orders $A$ in $M$, then $R$ well orders $A$ universally

Published on 12 Apr 2026 - 22:17

score 66 · Answer 7 · 2026-04-14 10:57:55

66

Views

Can the cardinality of the set of all intervening cardinals between sets and their power sets be always singular?

Published on 14 Apr 2026 - 10:57

score 194 · Answer 8 · 2026-04-13 21:06:12

194

Views

Zermelo's Proof of the Well Ordering Theorem

Published on 13 Apr 2026 - 21:06

score 116 · Answer 9 · 2026-04-12 15:17:04

Can set operations be set-theoretically defined as functions? ( Is there any set that could be the domain of these functions?)

score 58 · Answer 10 · 2026-04-10 12:25:16

58

Views

Does $V_n$ model union?

Published on 10 Apr 2026 - 12:25

score 195 · Answer 11 · 2026-04-14 01:13:14

195

Views

If $\omega_1$ is inaccessible to the reals, then every $\mathbf{\Sigma}_2^1$ set has the Baire property

Published on 14 Apr 2026 - 1:13

score 185 · Answer 12 · 2026-04-11 07:36:18

185

Views

For which $\alpha$ does $L_\alpha\models\omega_1$ is a cardinal?

Published on 11 Apr 2026 - 7:36

score 101 · Answer 13 · 2026-04-12 05:28:02

101

Views

What kind of infinity is the number of different infinities?

Published on 12 Apr 2026 - 5:28

score 71 · Answer 14 · 2026-04-12 02:27:37

71

Views

On the construction of the algebra of elementary embeddings $V_\delta\prec V_\delta$

Published on 12 Apr 2026 - 2:27

score 59 · Answer 15 · 2026-04-14 00:38:48

For a given set $S$ , is it possible to find a well ordered set $T$ such that every $S$ indexed subset of $T$ has a strict upper bound?

List Question

Proving that the boolean prime ideal theorem does not hold in a permutation model

Counterexample for $\prod_{i<\nu} \kappa_i=(\sup_{i<\nu}\kappa_i)^{\nu}$ when $\kappa_i$ is not an increasing $\nu$-sequence of cardinals

Models of set theory where not every set can be linearly ordered

Motivation of the von Neumann definition of ordinals

Is it possible that $\mathcal{X} = \mathcal{Y}$, yet $\mathcal{X} \in \mathcal{Y}$?

If $M$ is a transitive set and $R$ well orders $A$ in $M$, then $R$ well orders $A$ universally

Can the cardinality of the set of all intervening cardinals between sets and their power sets be always singular?

Zermelo's Proof of the Well Ordering Theorem

Can set operations be set-theoretically defined as functions? ( Is there any set that could be the domain of these functions?)

Does $V_n$ model union?

If $\omega_1$ is inaccessible to the reals, then every $\mathbf{\Sigma}_2^1$ set has the Baire property

For which $\alpha$ does $L_\alpha\models\omega_1$ is a cardinal?

What kind of infinity is the number of different infinities?

On the construction of the algebra of elementary embeddings $V_\delta\prec V_\delta$

For a given set $S$ , is it possible to find a well ordered set $T$ such that every $S$ indexed subset of $T$ has a strict upper bound?

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