Question

Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).

score 171 · Answer 1 · 2019-03-06 19:56:55

171

Views

Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).

Published on 06 Mar 2019 - 19:56

score 220 · Answer 2 · 2019-03-07 16:43:21

220

Views

Verifying axiom of substitution?

Published on 07 Mar 2019 - 16:43

score 57 · Answer 3 · 2026-03-25 20:24:40

57

Views

Basis of Mathematics

Published on 25 Mar 2026 - 20:24

score 501 · Answer 4 · 2026-03-12 09:10:05

501

Views

Axiom schemas vs second order axioms: which first-order predicates "exist"?

Published on 12 Mar 2026 - 9:10

score 115 · Answer 5 · 2026-03-25 21:22:07

115

Views

Finite axiomatization of second-order NBG

Published on 25 Mar 2026 - 21:22

score 142 · Answer 6 · 2019-03-16 23:35:49

142

Views

Why $x=x$? Why $x=y$ and $y=z$ imply $x=z$? (Assume, $x$, $y$ and $z$ are reals.)

Published on 16 Mar 2019 - 23:35

score 68 · Answer 7 · 2019-03-18 04:32:42

68

Views

Are these two extensionality-axioms equivalent?

Published on 18 Mar 2019 - 4:32

score 247 · Answer 8 · 2019-03-18 12:27:16

247

Views

Does the Axiom schema of Replacement imply the Axiom of Infinity?

Published on 18 Mar 2019 - 12:27

score 67 · Answer 9 · 2019-03-23 10:12:47

67

Views

ZFC - Prove existence of set {A_1, A_2, A_3, ...}

Published on 23 Mar 2019 - 10:12

score 265 · Answer 10 · 2019-03-24 18:53:47

265

Views

Why do the hereditarily finite sets model ZF-Infinity, if we need Infinity to talk about them?

Published on 24 Mar 2019 - 18:53

score 1.5k · Answer 11 · 2019-03-25 22:42:25

1.5k

Views

Vector space basics: scalar times a nonzero vector = zero implies scalar = zero?

Published on 25 Mar 2019 - 22:42

score 123 · Answer 12 · 2019-03-26 17:05:55

123

Views

Are axioms in mathematics comparable to hypotheses in experimental sciences?

Published on 26 Mar 2019 - 17:05

score 815 · Answer 13 · 2019-03-27 15:19:58

815

Views

What is the point of formalization in mathematics and how does it relate to axiomatization?

Published on 27 Mar 2019 - 15:19

score 783 · Answer 14 · 2019-03-30 16:10:54

783

Views

Why are the axiom of specification is an axiom schema? Why not just a single axiom?

Published on 30 Mar 2019 - 16:10

score 249 · Answer 15 · 2019-03-30 17:39:39

249

Views

Some questions about different axiomatic systems for neighbourhoods

Published on 30 Mar 2019 - 17:39

List Question

Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).

Verifying axiom of substitution?

Basis of Mathematics

Axiom schemas vs second order axioms: which first-order predicates "exist"?

Finite axiomatization of second-order NBG

Why $x=x$? Why $x=y$ and $y=z$ imply $x=z$? (Assume, $x$, $y$ and $z$ are reals.)

Are these two extensionality-axioms equivalent?

Does the Axiom schema of Replacement imply the Axiom of Infinity?

ZFC - Prove existence of set {A_1, A_2, A_3, ...}

Why do the hereditarily finite sets model ZF-Infinity, if we need Infinity to talk about them?

Vector space basics: scalar times a nonzero vector = zero implies scalar = zero?

Are axioms in mathematics comparable to hypotheses in experimental sciences?

What is the point of formalization in mathematics and how does it relate to axiomatization?

Why are the axiom of specification is an axiom schema? Why not just a single axiom?

Some questions about different axiomatic systems for neighbourhoods

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