A Note on Power-OTMs
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929690679181312 |
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| author | Carl, Merlin |
| author_facet | Carl, Merlin |
| contents | We consider the computational strength of Power-OTMs, i.e., ordinal Turing machines equipped with a power set operator, and study a notion of realizability based on these machines. When parameters are allowed, these machines are, modulo access to a global well-ordering, equivalent to the Set Register Machines defined by Robert Passmann in \cite{Passmann}, and while most of the results on the realizability of Power-OTMs are analogous to results obtained by Passmann, the settings lead to different results concerning the axiom of choice. As we will see, the computational strength of power-OTMs can, depending on the set-theoretical background, also differ from that of Set Register Machines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Power-OTMs Carl, Merlin Logic We consider the computational strength of Power-OTMs, i.e., ordinal Turing machines equipped with a power set operator, and study a notion of realizability based on these machines. When parameters are allowed, these machines are, modulo access to a global well-ordering, equivalent to the Set Register Machines defined by Robert Passmann in \cite{Passmann}, and while most of the results on the realizability of Power-OTMs are analogous to results obtained by Passmann, the settings lead to different results concerning the axiom of choice. As we will see, the computational strength of power-OTMs can, depending on the set-theoretical background, also differ from that of Set Register Machines. |
| title | A Note on Power-OTMs |
| topic | Logic |
| url | https://arxiv.org/abs/2412.03440 |