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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.

1 vote

Given a polynomial-time algorithm, can we compute an explicit polynomial time bound just fro...

Just to observe, also in view of Carl Mummert comment, that I used very similar techniques in my POPL'08 article "The intensional content of Rice's theorem". I call "complexity clique" a class of prog …
Andrea Asperti's user avatar
6 votes

Is simply typed lambda calculus with fixed-point combinator Turing-complete?

Damiano is right, the answer is no: it is not Turing complete. Supposing to define natural numbers as some type (o->o)->o->o, even with fixpoints you cannot define the predecessor (that would be eno …
Andrea Asperti's user avatar