Article
Version 10
Preserved in Portico This version is not peer-reviewed
Constructive Mathematics with the Predicate of the Current Mathematical Knowledge
Version 1
: Received: 27 July 2023 / Approved: 28 July 2023 / Online: 31 July 2023 (10:54:27 CEST)
Version 2 : Received: 2 August 2023 / Approved: 3 August 2023 / Online: 4 August 2023 (07:45:49 CEST)
Version 3 : Received: 14 August 2023 / Approved: 15 August 2023 / Online: 15 August 2023 (08:49:43 CEST)
Version 4 : Received: 29 August 2023 / Approved: 30 August 2023 / Online: 31 August 2023 (03:53:31 CEST)
Version 5 : Received: 5 September 2023 / Approved: 6 September 2023 / Online: 7 September 2023 (05:01:30 CEST)
Version 6 : Received: 20 September 2023 / Approved: 21 September 2023 / Online: 22 September 2023 (05:14:58 CEST)
Version 7 : Received: 9 October 2023 / Approved: 10 October 2023 / Online: 10 October 2023 (10:05:52 CEST)
Version 8 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 19 October 2023 (04:49:53 CEST)
Version 9 : Received: 4 December 2023 / Approved: 6 December 2023 / Online: 6 December 2023 (12:11:37 CET)
Version 10 : Received: 14 January 2024 / Approved: 16 January 2024 / Online: 16 January 2024 (06:42:23 CET)
Version 2 : Received: 2 August 2023 / Approved: 3 August 2023 / Online: 4 August 2023 (07:45:49 CEST)
Version 3 : Received: 14 August 2023 / Approved: 15 August 2023 / Online: 15 August 2023 (08:49:43 CEST)
Version 4 : Received: 29 August 2023 / Approved: 30 August 2023 / Online: 31 August 2023 (03:53:31 CEST)
Version 5 : Received: 5 September 2023 / Approved: 6 September 2023 / Online: 7 September 2023 (05:01:30 CEST)
Version 6 : Received: 20 September 2023 / Approved: 21 September 2023 / Online: 22 September 2023 (05:14:58 CEST)
Version 7 : Received: 9 October 2023 / Approved: 10 October 2023 / Online: 10 October 2023 (10:05:52 CEST)
Version 8 : Received: 17 October 2023 / Approved: 18 October 2023 / Online: 19 October 2023 (04:49:53 CEST)
Version 9 : Received: 4 December 2023 / Approved: 6 December 2023 / Online: 6 December 2023 (12:11:37 CET)
Version 10 : Received: 14 January 2024 / Approved: 16 January 2024 / Online: 16 January 2024 (06:42:23 CET)
A peer-reviewed article of this Preprint also exists.
Tyszka, A. Constructive Mathematics with the Predicate of the Current Mathematical Knowledge. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4710446. Tyszka, A. Constructive Mathematics with the Predicate of the Current Mathematical Knowledge. SSRN Electronic Journal 2024, doi:10.2139/ssrn.4710446.
Abstract
We assume that the current mathematical knowledge K is a finite set of statements from both formal and constructive mathematics, which is time-dependent and publicly available. Any formal theorem of any mathematician from past or present forever belongs to K. We assume that mathematical sets are atemporal entities. In this article, they exist formally in ZFC theory although their properties can be time-dependent (when they depend on K) or informal. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X ⊆ N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X.
Keywords
constructive mathematics; constructively defined algorithms; current mathematical knowledge; informal mathematics; known algorithms
Subject
Computer Science and Mathematics, Logic
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Apoloniusz Tyszka
Commenter's Conflict of Interests: Author
An older version of the preprint appeared in
Asian Research Journal of Mathematics 19 (2023), no. 12, pp. 69-79.
http://doi.org/10.9734/arjom/2023/v19i12773