Question

Does "All additive functions are linear" imply every set of reals is measurable?

score 657 · Answer 1 · 2021-01-01 04:03:01

657

Views

Does "All additive functions are linear" imply every set of reals is measurable?

Published on 01 Jan 2021 - 4:03

score 386 · Answer 2 · 2026-04-06 13:46:55

386

Views

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?

Published on 06 Apr 2026 - 13:46

score 143 · Answer 3 · 2021-01-03 14:19:14

143

Views

(Non)necessity of the axiom of choice in proving associativity of the tensor product

Published on 03 Jan 2021 - 14:19

score 33 · Answer 4 · 2021-01-03 19:42:56

33

Views

Is AC required to demonstrate that every collection of disjoint open intervals in R is countable?

Published on 03 Jan 2021 - 19:42

score 254 · Answer 5 · 2021-01-04 19:16:57

254

Views

Consequences of Axiom of Choice

Published on 04 Jan 2021 - 19:16

score 138 · Answer 6 · 2026-03-29 18:35:59

138

Views

Characterizing Vector Spaces without (provable) Basis in ZF

Published on 29 Mar 2026 - 18:35

score 102 · Answer 7 · 2026-03-29 20:06:19

102

Views

Product forcing of symmetric systems

Published on 29 Mar 2026 - 20:06

score 75 · Answer 8 · 2021-01-12 22:33:24

75

Views

Does "All additive functions are linear" imply every set of reals has the Baire property?

Published on 12 Jan 2021 - 22:33

score 364 · Answer 9 · 2021-01-14 20:10:54

364

Views

Strength of "Cofinite Choice"

Published on 14 Jan 2021 - 20:10

score 40 · Answer 10 · 2021-01-17 02:47:30

40

Views

Coding $\omega$-sequences of 0,1 with $\mathbb{Z}$-sequences of 0,1

Published on 17 Jan 2021 - 2:47

score 627 · Answer 11 · 2021-01-20 06:38:26

627

Views

Does ZF prove that there are more cardinals than elements of any set?

Published on 20 Jan 2021 - 6:38

score 84 · Answer 12 · 2021-01-20 18:03:41

If $A$ is an infinite set and $b \notin A$, is the equivalence $A \sim A \bigcup \{b\}$ provable without the axiom of choice (i.e. in ZF)?

score 373 · Answer 13 · 2026-04-01 13:32:51

373

Views

Dual of axiom of choice

Published on 01 Apr 2026 - 13:32

score 108 · Answer 14 · 2021-01-31 01:17:36

108

Views

Injection from $\mathbb{R}$ to $\mathbb{R}/\mathbb{Q}$

Published on 31 Jan 2021 - 1:17

score 53 · Answer 15 · 2026-02-23 08:33:55

53

Views

A fact about algebraic systems and axiom of choice

Published on 23 Feb 2026 - 8:33

List Question

Does "All additive functions are linear" imply every set of reals is measurable?

In ZF, does the ring of continuous functions $C([0,1], \mathbb{R})$ have prime ideals which is not maximal?

(Non)necessity of the axiom of choice in proving associativity of the tensor product

Is AC required to demonstrate that every collection of disjoint open intervals in R is countable?

Consequences of Axiom of Choice

Characterizing Vector Spaces without (provable) Basis in ZF

Product forcing of symmetric systems

Does "All additive functions are linear" imply every set of reals has the Baire property?

Strength of "Cofinite Choice"

Coding $\omega$-sequences of 0,1 with $\mathbb{Z}$-sequences of 0,1

Does ZF prove that there are more cardinals than elements of any set?

If $A$ is an infinite set and $b \notin A$, is the equivalence $A \sim A \bigcup \{b\}$ provable without the axiom of choice (i.e. in ZF)?

Dual of axiom of choice

Injection from $\mathbb{R}$ to $\mathbb{R}/\mathbb{Q}$

A fact about algebraic systems and axiom of choice

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