Question

What axioms are required to imply the existence of all conceivable subsets?

score 106 · Answer 1 · 2026-03-25 22:05:19

106

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What axioms are required to imply the existence of all conceivable subsets?

Published on 25 Mar 2026 - 22:05

score 185 · Answer 2 · 2020-06-13 18:34:41

185

Views

Is the following provable in Zermelo–Fraenkel Set Theory?

Published on 13 Jun 2020 - 18:34

score 72 · Answer 3 · 2020-06-14 13:12:25

72

Views

Show equivalence with BPI: every Boolean algebra has a prime ideal

Published on 14 Jun 2020 - 13:12

score 214 · Answer 4 · 2020-06-14 13:12:57

214

Views

Can a regular directed graph be axiomatized in first order Logic?

Published on 14 Jun 2020 - 13:12

score 48 · Answer 5 · 2020-06-15 22:42:57

48

Views

Are $X$ and $Y$ the same in these two equivalent formulations of the axiom of choice?

Published on 15 Jun 2020 - 22:42

score 195 · Answer 6 · 2020-06-25 12:12:33

195

Views

What constitutes a rigorous proof, and can intuitive explanations be made rigorous?

Published on 25 Jun 2020 - 12:12

score 116 · Answer 7 · 2020-06-30 19:37:01

116

Views

Group theory with one more axiom

Published on 30 Jun 2020 - 19:37

score 227 · Answer 8 · 2020-07-07 11:39:42

227

Views

Without the ZF axiom of regularity can any infinite sets be constructed?

Published on 07 Jul 2020 - 11:39

score 66 · Answer 9 · 2026-03-26 19:24:06

66

Views

Proving that $\mathbb{Z_{-}} \cap \mathbb{N}=\emptyset$

Published on 26 Mar 2026 - 19:24

score 136 · Answer 10 · 2020-07-10 07:48:30

136

Views

Probability axioms does not make sense?

Published on 10 Jul 2020 - 7:48

score 296 · Answer 11 · 2026-03-25 18:54:49

296

Views

Would unrestricted comprehension and no regularity avoid Russel's paradox with this modification?

Published on 25 Mar 2026 - 18:54

score 104 · Answer 12 · 2026-03-25 03:02:21

104

Views

Are there any sets of axioms that have an efficient algorithm for all provable statements?

Published on 25 Mar 2026 - 3:02

score 329 · Answer 13 · 2020-07-17 17:42:37

329

Views

I am trying to understand how sets are generally defined using ZF set theory.

Published on 17 Jul 2020 - 17:42

score 153 · Answer 14 · 2020-07-18 05:11:34

153

Views

How to use least upper bound principle to prove that monotonic functions at infinity are either infinity or real?

Published on 18 Jul 2020 - 5:11

score 141 · Answer 15 · 2020-07-20 16:50:56

141

Views

Is this an axiom? "For a square, in order to draw a straight line between opposite diagonals, the line needs to pass through the mid-point."

Published on 20 Jul 2020 - 16:50

List Question

What axioms are required to imply the existence of all conceivable subsets?

Is the following provable in Zermelo–Fraenkel Set Theory?

Show equivalence with BPI: every Boolean algebra has a prime ideal

Can a regular directed graph be axiomatized in first order Logic?

Are $X$ and $Y$ the same in these two equivalent formulations of the axiom of choice?

What constitutes a rigorous proof, and can intuitive explanations be made rigorous?

Group theory with one more axiom

Without the ZF axiom of regularity can any infinite sets be constructed?

Proving that $\mathbb{Z_{-}} \cap \mathbb{N}=\emptyset$

Probability axioms does not make sense?

Would unrestricted comprehension and no regularity avoid Russel's paradox with this modification?

Are there any sets of axioms that have an efficient algorithm for all provable statements?

I am trying to understand how sets are generally defined using ZF set theory.

How to use least upper bound principle to prove that monotonic functions at infinity are either infinity or real?

Is this an axiom? "For a square, in order to draw a straight line between opposite diagonals, the line needs to pass through the mid-point."

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