article · PhilPapers (PhilPapers Foundation)

A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K

Tyszka, Apoloniusz

Cited by 0Abstract and details only

Abstract

The theorem of Royer and Case states that there exists a limit-computable function β_1:N→N which eventually dominates every computable function δ_1:N→N. We present an alternative proof of this theorem. K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent and publicly available. Any theorem of any mathematician from past or present forever belongs to K. 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. We present both constructive and non-constructive proof of (1). Statement (1) claims that there exists a function f:N→N such that (f is computable in the limit)∧(¬K(f is computable))∧(¬K(f is uncomputable))∧(f eventually dominates every function δ:N→N with a single-fold Diophantine representation). Since Martin Davis' conjecture on single-fold Diophantine representations disproves Statement (1), Statement (1) justifies the title of the article.

Cite this paper

APA 7

Tyszka, A. (n.d.). A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K. PhilPapers (PhilPapers Foundation).

MLA 9

Tyszka, Apoloniusz. “A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K.” PhilPapers (PhilPapers Foundation).

Chicago

Tyszka, Apoloniusz. n.d.. “A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K.” PhilPapers (PhilPapers Foundation).

Harvard

Tyszka, A. (n.d.) ‘A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K’, PhilPapers (PhilPapers Foundation).

BibTeX

@article{tyszkatrue,
  title = {{A true mathematical statement Ψ with the predicate K of the current mathematical knowledge, where Ψ may be false in the future and does not express the current knowledge about the provability of any mathematical statements Ψ1,...,Ψn without K}},
  author = {Tyszka, Apoloniusz},
  journal = {PhilPapers (PhilPapers Foundation)}
}

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