MoL-2024-27: Stammes, Jasper (2024) Ordinal Reductions on Choice Principles. [Report]
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Abstract
In classical computability theory and computable analysis, two problems’ relative computability can be studied through several notions of reducibility. We wish to generalize a few of these notions. Instead of using a classical Turing machine, we consider a model of computation that can handle objects of any cardinality.
The Ordinal Turing Machine (OTM) is a generalization of the classical Turing machine, where computations have unbounded available time and space. In this thesis we will study the relative OTM-computability of construction problems arising from choice principles in set theory, based on similar work by Carl. We will use two existing notions of reducibility: OTM-reductions and ordinal Weihrauch reductions. We also define two similar reductions. In this setting, we prove the first known non-trivial case of OTM-irreducibility.
| Item Type: | Report |
|---|---|
| Report Nr: | MoL-2024-27 |
| Series Name: | Master of Logic Thesis (MoL) Series |
| Year: | 2024 |
| Subjects: | Logic Mathematics |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 10 Nov 2026 14:23 |
| Last Modified: | 10 Nov 2026 14:24 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2458 |
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