Article
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On One-Point Time on an Oriented Set
Version 1
: Received: 1 December 2022 / Approved: 5 December 2022 / Online: 5 December 2022 (11:27:04 CET)
How to cite: Grushka, Y. On One-Point Time on an Oriented Set. Preprints 2022, 2022120075. https://doi.org/10.20944/preprints202212.0075.v1 Grushka, Y. On One-Point Time on an Oriented Set. Preprints 2022, 2022120075. https://doi.org/10.20944/preprints202212.0075.v1
Abstract
The notion of oriented set is the basic elementary concept of the theory of changeable sets. The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. In the present paper the necessary and sufficient condition of the existence of one-point time on an oriented set is established. From the intuitive point of view, one-point time is the time associated with the evolution of a system consisting of only one object (for example, from one material point). Namely, it is proven that the one-point time exists on the oriented set if and only if this oriented set is a quasi-chain. Also, using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets.
Keywords
Oriented sets; changeable sets; time; ordered sets; axiom of choice
Subject
Computer Science and Mathematics, Mathematics
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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