Question

Bijection between real and natural numbers.

score 217 · Answer 1 · 2026-03-29 04:48:12

217

Views

Bijection between real and natural numbers.

Published on 29 Mar 2026 - 4:48

score 125 · Answer 2 · 2026-03-28 07:16:34

125

Views

Let $\alpha$ be a limit ordinal. $f: \alpha \to \beta $ be strictly increase cofinal map. then $cf(\alpha) = cf(\beta)$.

Published on 28 Mar 2026 - 7:16

score 227 · Answer 3 · 2020-06-09 20:43:59

227

Views

Which sets have nontrivial elementary extensions (with respect to all possible relations) of the same cardinality?

Published on 09 Jun 2020 - 20:43

score 111 · Answer 4 · 2020-06-10 01:42:30

111

Views

Uncoutable set minus a countable subset is uncountable without axiom of choice or continuum hypothesis

Published on 10 Jun 2020 - 1:42

score 25 · Answer 5 · 2020-06-10 07:05:40

25

Views

Suppose that $S\sim T$, $P\sim Q$, $S⋂P=\varnothing $ and $T⋂Q=\varnothing$. Prove that $(S∪P) \sim (T∪Q)$.

Published on 10 Jun 2020 - 7:05

score 35 · Answer 6 · 2020-06-10 07:52:32

35

Views

Let S, T and P be three nonempty set. Prove that (a)S~S (b)If S~T, then T~S

Published on 10 Jun 2020 - 7:52

score 245 · Answer 7 · 2026-03-26 07:59:07

245

Views

Forcing $2^{\omega} = \omega_{\omega_1}$ together with $2^{\omega_1} = \omega_{\omega_2}$

Published on 26 Mar 2026 - 7:59

score 30 · Answer 8 · 2026-03-30 13:24:52

30

Views

Unknown index in a model theoretic considerations

Published on 30 Mar 2026 - 13:24

score 34 · Answer 9 · 2020-06-11 20:48:08

34

Views

$(\lambda,D)$-model homogenity

Published on 11 Jun 2020 - 20:48

score 138 · Answer 10 · 2020-06-12 00:00:42

138

Views

Proving that ${\aleph_1}^{\aleph_0}\leq |[\omega_1]^{\omega}|$

Published on 12 Jun 2020 - 0:00

score 81 · Answer 11 · 2026-03-28 07:16:40

81

Views

Given $\kappa = \sup_{\alpha< \lambda} \kappa_{\alpha}$n can we assume the $\{\kappa_\alpha: \alpha < \lambda\}$ is strictly increasing?

Published on 28 Mar 2026 - 7:16

score 72 · Answer 12 · 2020-06-14 15:44:35

72

Views

Explanation of Cardinal Arithmetic Used in Proving that bases of Vector spaces have the same cardinality.

Published on 14 Jun 2020 - 15:44

score 125 · Answer 13 · 2020-06-15 09:16:07

125

Views

Let $G$ be the group of all the maps from closed interval $[0,1]$ to $\mathbb{Z}$.

Published on 15 Jun 2020 - 9:16

score 220 · Answer 14 · 2020-06-15 09:24:45

220

Views

How to prove $|{^A}{(K \times L)}| =_c |{^A}{K} \times {^A}{L}|$?

Published on 15 Jun 2020 - 9:24

score 38 · Answer 15 · 2020-06-15 15:29:29

38

Views

$ (\prod_{i\in I}\kappa_i)^\mu = \prod_{i\in I}\kappa_i^\mu $, where $ \kappa_i ,\mu $ are infinite cardinals, $I$ an infinite set.

Published on 15 Jun 2020 - 15:29

List Question

Bijection between real and natural numbers.

Let $\alpha$ be a limit ordinal. $f: \alpha \to \beta $ be strictly increase cofinal map. then $cf(\alpha) = cf(\beta)$.

Which sets have nontrivial elementary extensions (with respect to all possible relations) of the same cardinality?

Uncoutable set minus a countable subset is uncountable without axiom of choice or continuum hypothesis

Suppose that $S\sim T$, $P\sim Q$, $S⋂P=\varnothing $ and $T⋂Q=\varnothing$. Prove that $(S∪P) \sim (T∪Q)$.

Let S, T and P be three nonempty set. Prove that (a)S~S (b)If S~T, then T~S

Forcing $2^{\omega} = \omega_{\omega_1}$ together with $2^{\omega_1} = \omega_{\omega_2}$

Unknown index in a model theoretic considerations

$(\lambda,D)$-model homogenity

Proving that ${\aleph_1}^{\aleph_0}\leq |[\omega_1]^{\omega}|$

Given $\kappa = \sup_{\alpha< \lambda} \kappa_{\alpha}$n can we assume the $\{\kappa_\alpha: \alpha < \lambda\}$ is strictly increasing?

Explanation of Cardinal Arithmetic Used in Proving that bases of Vector spaces have the same cardinality.

Let $G$ be the group of all the maps from closed interval $[0,1]$ to $\mathbb{Z}$.

How to prove $|{^A}{(K \times L)}| =_c |{^A}{K} \times {^A}{L}|$?

$ (\prod_{i\in I}\kappa_i)^\mu = \prod_{i\in I}\kappa_i^\mu $, where $ \kappa_i ,\mu $ are infinite cardinals, $I$ an infinite set.

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