A falsifiable statement Ψ of the form "∃f:N→N of unknown computability such that ...", where ZFC expresses Ψ at any time and Ψ significantly strengthens a non-trivial mathematical theorem
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| dc.contributor.author | Tyszka, Apoloniusz | |
|---|---|---|
| dc.contributor.organization | Hugo Kołłątaj University | |
| dc.date.accessioned | 2024-12-13T13:58:27Z | |
| dc.date.available | 2024-12-13T13:58:27Z | |
| dc.date.issued | 2024-12-13 | |
| dc.description.abstract | We present a new constructive proof of the following theorem: there exists a limit-computable function β_1:N→N which eventually dominates every computable function δ_1:N→N. We prove: (1) there exists a limit-computable function f:N→N of unknown computability which eventually dominates every function δ:N→N with a single-fold Diophantine representation, (2) statement (1) significantly strengthens a non-trivial mathematical theorem, (3) Martin Davis' conjecture on single-fold Diophantine representations disproves (1), (4) ZFC expresses (1) at any time. We present both constructive and non-constructive proof of (1). | en |
| dc.identifier.citation | Tyszka, Apoloniusz, A falsifiable statement Ψ of the form "∃f:N→N of unknown computability such that ...", where ZFC expresses Ψ at any time and Ψ significantly strengthens a non-trivial mathematical theorem (December 13, 2024). Available at SSRN: https://ssrn.com/abstract=4710446 or http://dx.doi.org/10.2139/ssrn.4710446 | |
| dc.identifier.doi | 10.2139/ssrn.4710446 | |
| dc.identifier.uri | https://open.icm.edu.pl/handle/123456789/25175 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.rights | Dozwolony użytek | |
| dc.source | SSRN Electronic Journal | |
| dc.subject | eventual domination | en |
| dc.subject | limit-computable function | en |
| dc.subject | predicate K of the written down mathematical knowledge | en |
| dc.subject | single-fold Diophantine representation | en |
| dc.subject | time-dependent truth in mathematics with the predicate K of the written down mathematical knowledge | en |
| dc.title | A falsifiable statement Ψ of the form "∃f:N→N of unknown computability such that ...", where ZFC expresses Ψ at any time and Ψ significantly strengthens a non-trivial mathematical theorem | en |
| dc.type | article | |
| dc.type.version | publishedVersion | |
| person.identifier.orcid | Tyszka, Apoloniusz [0000-0002-2770-5495] |
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