MoL-2023-25: Priority arguments in transfinite computability theory

MoL-2023-25: Hegeman, Steef (2023) Priority arguments in transfinite computability theory. [Report]

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The priority method has been used to examine the structure of the semi-decidable degrees in computability theory. We discuss three classical results (the Friedberg-Muchnik theorem, the splitting theorem, and the thickness lemma) and discuss whether their proofs could be adapted to transfinite computability theory, specifically to the machine models of ITTMs, α-machines, and p-α-machines (α-machines equipped an extra ordinal parameter). We prove a splitting theorem for certain ITTM-semi-decidable sets—sufficient to conclude that there are infinitely many ITTM-semi-decidable degrees—and a thickness lemma for certain ITTM-semi-decidable sets of low degree. We sketch results for α-machines and p-OTMs (ordinal Turing machines with an extra parameter), among which a splitting theorem and a thickness lemma for p-OTMs.

Item Type: Report
Report Nr: MoL-2023-25
Series Name: Master of Logic Thesis (MoL) Series
Year: 2023
Subjects: Logic
Depositing User: Dr Marco Vervoort
Date Deposited: 24 Oct 2023 13:03
Last Modified: 24 Oct 2023 13:03

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