Infinite time computable model theory

Daniel Seabold (Hofstra University); Joel David Hamkins (The City University of New York); Russell Miller (The City University of New York); Steve Warner (Hofstra University)

arxiv: math/0602483 · v1 · submitted 2006-02-22 · 🧮 math.LO

Infinite time computable model theory

Joel David Hamkins (The City University of New York) , Russell Miller (The City University of New York) , Daniel Seabold (Hofstra University) , Steve Warner (Hofstra University) This is my paper

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keywords timeinfinitecomputabletheorymodelanaloguearisingbuilt

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We introduce infinite time computable model theory, the computable model theory arising with infinite time Turing machines, which provide infinitary notions of computability for structures built on the reals R. Much of the finite time theory generalizes to the infinite time context, but several fundamental questions, including the infinite time computable analogue of the Completeness Theorem, turn out to be independent of ZFC.

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Infinite time computable model theory

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