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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.

6 votes

Succinctly naming big numbers: ZFC versus Busy-Beaver

This isn't an answer, but it's too long for a comment. I don't think the computable ordinals are well enough defined for the function $f(n)$ to work. Suppose you give me a system mapping {$0,1$}$^* $ …
Peter Shor's user avatar
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4 votes

Succinctly naming big numbers: ZFC versus Busy-Beaver

I have another question which is too long to fit into a comment: how do you even know that $f(n)$ is increasing? If you have two Turing Machines $M$ and $M'$ that realize the same ordinal $\alpha$, …
Peter Shor's user avatar
  • 6,342