Set Theory and Logic

2102 Submissions

[2] viXra:2102.0121 [pdf] replaced on 2021-03-30 14:11:16

Infinity Put to the Test: Towards a Discrete Revolution in the Mathematics of the XXI Century

Authors: Antonio Leon
Comments: 404 Pages.

From different areas of mathematics, such as set theory, geometry, transfinite arithmetic or supertask theory, in this book more than forty arguments are developed about the inconsistency of the hypothesis of the actual infinity in contemporary mathematics. A hypothesis according to which the uncompletable lists, as the list of the natural numbers, exist as completed lists. The inconsistency of this hypothesis would have an enormous impact on physics, forcing us to change the continuum space-time for a discrete model, with indivisible units (atoms) of space and time. The discrete model would be a great simplification of physical theories, including relativity and quantum mechanics. It would also suppose the solution of the old problem of change, posed by the pre-Socratics philosophers twenty-seven centuries ago.
Category: Set Theory and Logic

[1] viXra:2102.0072 [pdf] replaced on 2021-02-18 16:36:18

Set Theory INC# Based on Intuitionistic Logic with Restricted Modus Ponens Rule

Authors: Jaykov Foukzon
Comments: 16 Pages. Journal of Advances in Mathematics and Computer Science, 36(2), 73-88. https://doi.org/10.9734/jamcs/2021/v36i230339

In this article Russell's paradox and Cantors paradox resolved successfully using intuitionistic logic with restricted modus ponens rule.
Category: Set Theory and Logic