2021
DOI: 10.2139/ssrn.3785977
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Fermat’s last theorem proved in Hilbert arithmetic. I. From the proof by induction to the viewpoint of Hilbert arithmetic

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Cited by 7 publications
(12 citation statements)
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References 116 publications
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“…Another impressive example can be "Fermat arithmetic" naively not distinguishing a finite arithmetic series consisting of any natural number of members from their set able to be infinite. One can demonstrate that Fermat's last theorem is a provable statement in that Fermat arithmetic, but it is unprovable in the contemporary standard mathematics underlain by both arithmetic and set theory since they imply a Gödel-like insolubility in relation to Fermat's last theorem, which can be demonstrated by means of its interpretation in terms of Yablo's paradox (Penchev 2021 March 9). Anyway, it can be proven in a more powerful mathematics able to overcome any Gödellike insolubility and among which Wiles's proof of Fermat's last theorem is to be enumerated though implicitly, but necessarily just because of the relevance of Yablo's paradox to Fermat's last theorem 18 .…”
Section: A Few More Doubts About the Gödel Incompleteness Statement: ...mentioning
confidence: 98%
See 1 more Smart Citation
“…Another impressive example can be "Fermat arithmetic" naively not distinguishing a finite arithmetic series consisting of any natural number of members from their set able to be infinite. One can demonstrate that Fermat's last theorem is a provable statement in that Fermat arithmetic, but it is unprovable in the contemporary standard mathematics underlain by both arithmetic and set theory since they imply a Gödel-like insolubility in relation to Fermat's last theorem, which can be demonstrated by means of its interpretation in terms of Yablo's paradox (Penchev 2021 March 9). Anyway, it can be proven in a more powerful mathematics able to overcome any Gödellike insolubility and among which Wiles's proof of Fermat's last theorem is to be enumerated though implicitly, but necessarily just because of the relevance of Yablo's paradox to Fermat's last theorem 18 .…”
Section: A Few More Doubts About the Gödel Incompleteness Statement: ...mentioning
confidence: 98%
“…Indeed, if one considers the preliminary choice as a meta-choice to the explicit choice, this would generate an hierarchy (or for example, a temporal series of choices) ad lib, which in turn can be equivalently interpreted as a single idempotent pair such as the opposition of any statement and its negation and thoroughly representable by a bit of information (in much more detail in: Penchev 2022 June 30; Penchev 2022 May 11;Penchev 2021 March 9).…”
Section: A Few More Doubts About the Gödel Incompleteness Statement: ...mentioning
confidence: 99%
“…as a mathematical statement needing a relevant proof what the nonstandard bijection (discussed in detail in other pares, e.g. Penchev 2022 June 30;2022 May 11;2022 March 11) quantum-mechanical description to the description of the same system in classical mechanics) inherently conditioning incompleteness, the explicit contradiction of their mutual anti-isometry appears immediately.…”
Section: The Gödel Incompleteness Versus the Gentzen Completeness By ...mentioning
confidence: 99%
“…Thus, the former generalizes the latter describing the transition from an infinite set to a finite set rather than a finite set as an ultimate result (being "ready-for-use") meant explicitly by Peano arithmetic by its fundamental concept of "natural number". In other words, that Dedekind-like finiteness means the process of how Peano arithmetic appears from any infinite set, or speaking loosely, from infinity just as Hilbert arithmetic in a wide sense means (for example, in relation to that: Fermat's last theorem to be proved : Penchev 2022 June 30;2022 May 11;2022 March 11).…”
Section: The Dedekind-like Bijection Of Infinite Sets Into Finite Set...mentioning
confidence: 99%
“…as a mathematical statement needing a relevant proof what the nonstandard bijection (discussed in detail in other pares, e.g. Penchev 2022 June 30;2022 May 11;2022 March 11) can deliver by its two dual "directions":…”
Section: The Gödel Incompleteness Versus the Gentzen Completeness By ...mentioning
confidence: 99%