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13
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1answer
1k views

Proof theoretic ordinal

In Ordinal Analysis, Proof-theoretic Ordinal of a theory is thought as measure of a consistency strength and computational power. Is it always the case? I. e. are there some general results about ...
1
vote
1answer
258 views

center depth of Birkhoff center

I saw a statement about the Birkhoff center. Namely let $X$ be a compact metric space and $f:X\to X$ be a homeomorphism on $X$. Then for each ordinal $\alpha$ we define for $\alpha=0$, let ...
5
votes
1answer
307 views

value of Theta in ZF+AD

Since I found out about it, I've always been interested in the Axiom of Determinacy rather than the Axiom of Choice. Along these lines, I've kept flipping back to ...
1
vote
0answers
301 views

Transfinite Sums Related to a Sequence

Hello, Given a sequence $S$ indexed by the finite ordinals, a limit ordinal $\alpha$, and $k \in \mathbb{N}$, define $S_{\alpha+k}$(the extension of $S$ to $\alpha+k$) to be the sum over the products ...
7
votes
5answers
1k views

What is the idea behind stationary sets?

Let $\kappa$ be a cardinal (of uncountable cofinality). A subset $S \subseteq \kappa$ is called stationary if it intersects every club, i.e. closed unbounded subset of $\kappa$. Now my question is ...
13
votes
7answers
1k views

Finding the largest integer describable with a string of symbols of predefined length

(This question is motivated by the reading of the article Large numbers and unprovable theorems by Joel Spencer, which can be found at ...