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Infinite time computable model theory

2006/02/22 by Joel David Hamkins, Russell Miller, Hamkins, Joel David +6
Computer Science · Mathematics · #03C57 #03D45 #03D60 #03E15 #Algorithms and Data Compression #Cellular Automata and Applications #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03C57 #msc:03D45 #msc:03D60 #msc:03E15

paper · pdf · doi:10.48550/arxiv.math/0602483

32 pages

arxiv created 2006/02/22 · openalex publication_date 2006/02/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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