List questions from ordinals | MathQA

Let $(\alpha_\xi\mid\xi<\kappa)$ be a sequence such that $\{\alpha_\xi\mid\xi<\kappa\}=\alpha$. Find an increasing subsequence that has limit $\alpha$

Published on 27 Dec 2018 - 3:15

A question regarding Brian M. Scott's proof that $\text{cf}(\aleph_{\omega_1})=\omega_1$

Published on 27 Dec 2018 - 16:31

What is the source of formal descriptions for large uncomputable ordinals clockable by Infinite Time Turing Machines?

Published on 25 Mar 2026 - 13:56

Is my understanding of a proof from textbook Introduction to Set Theory by Hrbacek and Jech correct?

Published on 29 Dec 2018 - 5:02

Is my understanding of this proof about cardinality correct?

Published on 29 Dec 2018 - 11:33

A question about a proof of Hausdorff's Formula

Published on 30 Dec 2018 - 3:42

Let $α$ and $β$ be ordinals such that $α>1$ and $β\neq0$. Let $γ$, $ζ$, and $η$ be ordinals st $γ<β$, $ζ<α$, and $η<α^{γ}$. Prove $α^γ ζ+η<α^{β}$.

Published on 04 Jan 2019 - 16:42

On proving $\omega^{\epsilon} = \epsilon$

Published on 19 Jan 2019 - 13:39

Proving nicely that $3+\omega=\omega$ where $\omega$ is the smallest limit ordinal.

Published on 22 Jan 2019 - 13:03

$\operatorname{card}(\bigcup\limits_{n \in \mathbb{N}} \underbrace{A\times...\times A}_{n})=k$ if $\operatorname{card}(A)=k$ infinite.

Published on 23 Jan 2019 - 20:28

Where is the theorem related to the construction of countable admissible ordinals by Turing machines with oracles?

Published on 22 Mar 2026 - 17:48

Does every countable well-order inject into the real numbers?

Published on 31 Jan 2019 - 11:45

How to use transfinite induction/recursion to construct a dense Hamel Basis of a Banach space?

Published on 07 Feb 2019 - 4:27

Set theory ordinal proof practice problem

Published on 08 Feb 2019 - 11:12

Isomorphism from limit ordinals to ordinals: is there a fixed point?

Published on 25 Mar 2026 - 20:36