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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.

6 votes
3 answers
599 views

Do "seemingly impossible functional programs" work with arrow types interpreted as Turing ma...

The title is a reference to this article by Martin Escardo, referring to work by originally by Ulrich Berger. It occurred that the programs described in this article can interpreted in the Turing mach …
Itai Bar-Natan's user avatar
4 votes

The problem of finding the first digit in Graham's number

In general, the first digit of a number $A$ can be determined from the fractional part of $\log_{10} A$. Specifically, if $\log_{10} A = n + \gamma$ where $n = \lfloor \log_{10} A \rfloor$ and $\gamma …
Itai Bar-Natan's user avatar