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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.

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Complexity of representations of sets using elementary functions

Fermat conjectured that $2^{2^n}+1$ is prime for every $n \in \mathbb{N}.$ Before even knowing about Euler's counterexample (that $2^{32}+1 = 641 \cdot 6700417$), you could possibly say that Fermat wa …