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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.

5 votes
1 answer
366 views

Why restrict to $\Sigma_1^0$ formulas in $RCA_0$ induction?

I recently asked this question over on math.se, warmly welcomed by crickets. I hope it's appropriate here. I'm reading Stillwell's Reverse Mathematics, and the induction axiom was just introduced. …
12 votes
2 answers
1k views

Why can Diophantine equations represent exponential growth?

The wikipedia page on Matiyasevich's theorem challenges: Unfortunately there seems to be as yet no short intuitive explanation as to why Diophantine equations can represent exponential growth only …