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Keith Millar

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19 Questions

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676

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Is this Variation of the Continuum Hypothesis Inconsistent with ZFC or ZF?

Feb 18 '18 at 13:42 Mohammad Golshani 27.6k

votes

answers

views

Formalizations of The Matchstick Diagram Representation of Ordinals

set-theory ordinal-numbers ordinal-analysis

Dec 1 '17 at 13:59 Gro-Tsen 16.2k

votes

answer

413

views

Is the smallest $L_\alpha$ with undefinable ordinals always countable?

set-theory lo.logic constructibility

Sep 5 '18 at 8:43 Ralf Schindler 1,488

votes

answer

395

views

Can the category of partial orders be fully embedded in the category of linear orders?

ct.category-theory set-theory large-cardinals

Dec 8 at 18:15 Keith Millar 1,098

votes

answers

142

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How much choice is required for a countably-infinite index subgroup of the real additive group?

gr.group-theory set-theory lo.logic descriptive-set-theory axiom-of-choice

Nov 1 at 17:57 YCor 37.9k

votes

answers

230

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On $ORD$ “satisfying” large cardinal properties

set-theory large-cardinals

Oct 31 '17 at 2:12 Keith Millar 1,098

votes

answers

775

views

“Antiforcing” - Is there a method to 'remove' sets from a model of ZF?

set-theory lo.logic forcing

Jul 4 '19 at 20:33 Master 550

votes

answer

160

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If $j:V\prec M$ has critical point $κ$ and for any $X\in M$ with $|X|=μ$, $|X|^M=μ$, what properties does $κ$ have?

set-theory large-cardinals ultrapowers

Oct 5 '18 at 10:23 Yair Hayut 4,378

votes

answer

210

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Weaker forms of Vopěnka's principle (using Indiscernables and other forms of Elementarity): How weak are they?

set-theory model-theory large-cardinals

Nov 5 '17 at 1:22 Joel David Hamkins 181k

votes

answer

303

views

How expressive can $\mathcal{L}_{\kappa,\kappa}$ be?

set-theory large-cardinals infinitary-logic

Nov 3 '17 at 16:46 Joel David Hamkins 181k

votes

answers

126

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If any satisfiable $\mathcal{L}_{κ,κ}(Q_{=κ})$-theory remains satisfiable when replacing $Q_{=κ}$ with $Q_{=μ}$, is $κ$ huge?

set-theory lo.logic model-theory large-cardinals

Oct 16 '18 at 14:44 Keith Millar 1,098

votes

answers

257

views

How Rowbottom can $\aleph_{\omega}$ be?

set-theory large-cardinals

Dec 16 '17 at 18:05 Keith Millar 1,098

votes

answers

282

views

Strong limit cardinals in AD

set-theory determinacy

Dec 12 '17 at 13:55 Noah Schweber 29.2k

votes

answer

347

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A weakening of cardinal compactness - is it equivalent?

set-theory model-theory large-cardinals

Sep 6 '18 at 14:14 Keith Millar 1,098

votes

answer

225

views

Elementary extensions of infinitary languages

set-theory large-cardinals infinitary-logic

Oct 27 '17 at 14:38 Kameryn Williams 660

vote

answers

237

views

Bernays' Reflection Principle Holding in Ranks?

set-theory large-cardinals

Jun 21 at 21:23 Yven Johannes Leist 5

vote

answer

257

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Under ZF + DC + AD, is it known what the properties are of the Hartogs number for $\mathcal{P}(\kappa)$ for some $\kappa>\aleph_0$?

set-theory determinacy

Oct 18 '17 at 16:09 Community♦ 1

votes

answer

197

views

What strengthenings of measurability do the Mostowski collapses of ultrapowers possess?

set-theory large-cardinals ultrapowers

Nov 6 '17 at 23:51 Keith Millar 1,098

votes

answer

338

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On The Explicit-Ness of $\omega_1$

lo.logic set-theory model-theory

Oct 15 '17 at 15:32 Todd Trimble♦ 47.7k

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19 Questions

Is this Variation of the Continuum Hypothesis Inconsistent with ZFC or ZF?

Formalizations of The Matchstick Diagram Representation of Ordinals

Is the smallest $L_\alpha$ with undefinable ordinals always countable?

Can the category of partial orders be fully embedded in the category of linear orders?

How much choice is required for a countably-infinite index subgroup of the real additive group?

On $ORD$ “satisfying” large cardinal properties

“Antiforcing” - Is there a method to 'remove' sets from a model of ZF?

If $j:V\prec M$ has critical point $κ$ and for any $X\in M$ with $|X|=μ$, $|X|^M=μ$, what properties does $κ$ have?

Weaker forms of Vopěnka's principle (using Indiscernables and other forms of Elementarity): How weak are they?

How expressive can $\mathcal{L}_{\kappa,\kappa}$ be?

If any satisfiable $\mathcal{L}_{κ,κ}(Q_{=κ})$-theory remains satisfiable when replacing $Q_{=κ}$ with $Q_{=μ}$, is $κ$ huge?

How Rowbottom can $\aleph_{\omega}$ be?

Strong limit cardinals in AD

A weakening of cardinal compactness - is it equivalent?

Elementary extensions of infinitary languages

Bernays' Reflection Principle Holding in Ranks?

Under ZF + DC + AD, is it known what the properties are of the Hartogs number for $\mathcal{P}(\kappa)$ for some $\kappa>\aleph_0$?

What strengthenings of measurability do the Mostowski collapses of ultrapowers possess?

On The Explicit-Ness of $\omega_1$