User Ldddd

10 votes

1 answer

810 views

Linking the Analysis of the Baire space, Cantor space and $\mathbb{R}$.

asked Aug 10, 2019 at 7:09

8 votes

0 answers

452 views

$\lt_{ip}$ is a well-defined well-ordering of iterable set premice.

asked Oct 30, 2019 at 11:10

8 votes

2 answers

268 views

Does the existence of a minimal cover for a subset of reals need some form of choice?

asked Aug 12, 2020 at 16:59

7 votes

0 answers

176 views

Dual notions of current large cardinals

asked Jun 27, 2021 at 9:46

6 votes

1 answer

196 views

On the beginnings and motivations of certain branches of set theory

asked Feb 21, 2020 at 9:56

6 votes

0 answers

155 views

Weak compactness equivalent

asked Mar 13, 2020 at 20:10

5 votes

1 answer

136 views

Coding a well-ordering of $2^{|\gamma|^{\lt \kappa}}$ in $P(P(P_\kappa\gamma))$ while preserving relative constructible hierarchy

asked Dec 25, 2019 at 11:19

5 votes

1 answer

214 views

If countable fragments of an ultrapower can be realized, then the ultrafilter is $\omega_1$-complete

asked Nov 5, 2020 at 16:00

5 votes

1 answer

187 views

Linear iterability for set models of $\mathsf{ZFC}$

asked Nov 9, 2020 at 15:26

5 votes

1 answer

121 views

Iterated projecta and their respective iterated Skolem functions

asked Apr 2, 2021 at 14:55

5 votes

3 answers

180 views

The Boolean-valued model $V^B$ is extensional.

asked Jul 19, 2018 at 13:31

5 votes

0 answers

135 views

If $\mathbb{P}$ is an infinite notion of forcing then there is $H\subset \mathbb{P}$ such that $M[H]$ is not a model of ZFC.

asked Aug 28, 2018 at 18:33

4 votes

1 answer

149 views

Reduction of the satisfaction relation for iterated ultrapowers to that of the first stage and formulas concerning finite product ultrafilters.

asked Oct 19, 2019 at 12:15

4 votes

1 answer

115 views

Existence of solidity witness implies the existence of standard solidity witness

asked Apr 13, 2021 at 12:34

4 votes

1 answer

150 views

Length of an extender in the iteration tree game is less than the support of the last extender in the respective premouse

asked May 23, 2021 at 12:04

4 votes

1 answer

119 views

For an extender $F$ of minimal length witnessing the coherence condition of a Martin-Steel Doddage, $\kappa_F = \iota_F$

asked Jun 29, 2021 at 13:25

4 votes

1 answer

151 views

Why do we require soundness for fine structural ultrapowers?

asked Oct 29, 2021 at 14:34

4 votes

1 answer

114 views

Proof of the incompatibility of extenders in comparison lemma of mice

asked May 29, 2021 at 11:34

4 votes

1 answer

356 views

An elementary embedding which fixes the ordinals, but is not the identity.

asked Nov 15, 2020 at 20:35

4 votes

1 answer

112 views

Ways to construct set models of $\mathsf{ZFC}$ from existing ones

asked Dec 2, 2020 at 17:18

4 votes

2 answers

257 views

AST is conservative over ZF

asked Apr 19, 2020 at 17:52

4 votes

1 answer

239 views

Definition of a simple function in fine structure theory

asked Mar 18, 2020 at 21:57

3 votes

1 answer

190 views

Definable subsets of the J-hierarchy in fine structure theory

asked Mar 24, 2020 at 18:19

3 votes

1 answer

230 views

$AC_\omega(^\omega\omega)$ implies that $\omega_1$ is regular.

asked Mar 5, 2020 at 12:06

3 votes

1 answer

64 views

Writing down a formula for "X is meager" in second order arithmetic with low complexity

asked Mar 11, 2020 at 14:20

3 votes

1 answer

172 views

Showing that extenders do not have nice closure properties

asked Feb 7, 2020 at 11:17

3 votes

1 answer

103 views

Existence of a surjective map $h:\alpha\rightarrow [\alpha]^{\lt\omega}$ such that $h \in \tilde{\Sigma}_1^{J_\alpha[E]}$

asked Apr 21, 2020 at 11:26

3 votes

1 answer

77 views

Properties of the spaces associated to the uniform ultrafilters of an extender

asked Jun 11, 2021 at 18:29

3 votes

1 answer

227 views

Counterexamples to the Weak Unique Branch Hypothesis and Weak $(\omega_1+1)$-Iteration Hypothesis

asked Jun 11, 2021 at 18:41

3 votes

0 answers

138 views

Different formalizations of fine structural concepts

asked Apr 25, 2021 at 8:56

Stack Exchange Network

75 Questions

Linking the Analysis of the Baire space, Cantor space and $\mathbb{R}$.

$\lt_{ip}$ is a well-defined well-ordering of iterable set premice.

Does the existence of a minimal cover for a subset of reals need some form of choice?

Dual notions of current large cardinals

On the beginnings and motivations of certain branches of set theory

Weak compactness equivalent

Coding a well-ordering of $2^{|\gamma|^{\lt \kappa}}$ in $P(P(P_\kappa\gamma))$ while preserving relative constructible hierarchy

If countable fragments of an ultrapower can be realized, then the ultrafilter is $\omega_1$-complete

Linear iterability for set models of $\mathsf{ZFC}$

Iterated projecta and their respective iterated Skolem functions

The Boolean-valued model $V^B$ is extensional.

If $\mathbb{P}$ is an infinite notion of forcing then there is $H\subset \mathbb{P}$ such that $M[H]$ is not a model of ZFC.

Reduction of the satisfaction relation for iterated ultrapowers to that of the first stage and formulas concerning finite product ultrafilters.

Existence of solidity witness implies the existence of standard solidity witness

Length of an extender in the iteration tree game is less than the support of the last extender in the respective premouse

For an extender $F$ of minimal length witnessing the coherence condition of a Martin-Steel Doddage, $\kappa_F = \iota_F$

Why do we require soundness for fine structural ultrapowers?

Proof of the incompatibility of extenders in comparison lemma of mice

An elementary embedding which fixes the ordinals, but is not the identity.

Ways to construct set models of $\mathsf{ZFC}$ from existing ones

AST is conservative over ZF

Definition of a simple function in fine structure theory

Definable subsets of the J-hierarchy in fine structure theory

$AC_\omega(^\omega\omega)$ implies that $\omega_1$ is regular.

Writing down a formula for "X is meager" in second order arithmetic with low complexity

Showing that extenders do not have nice closure properties

Existence of a surjective map $h:\alpha\rightarrow [\alpha]^{\lt\omega}$ such that $h \in \tilde{\Sigma}_1^{J_\alpha[E]}$

Properties of the spaces associated to the uniform ultrafilters of an extender

Counterexamples to the Weak Unique Branch Hypothesis and Weak $(\omega_1+1)$-Iteration Hypothesis

Different formalizations of fine structural concepts