Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals

Details Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals

2011-01-10

arxiv.org/abs/1101.1864v1

Mathematics

Logic

Submitted to the Effective Mathematics of the Uncountable Conference, 2009

Scientific paper

We describe the basic theory of infinite time Turing machines and some recent developments, including the infinite time degree theory, infinite time complexity theory, and infinite time computable model theory. We focus particularly on the application of infinite time Turing machines to the analysis of the hierarchy of equivalence relations on the reals, in analogy with the theory arising from Borel reducibility. We define a notion of infinite time reducibility, which lifts much of the Borel theory into the class $\bm{\Delta}^1_2$ in a satisfying way.

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