Set Theory and Logic

2307 Submissions

[3] viXra:2307.0110 [pdf] submitted on 2023-07-22 21:50:45

Some Notes on Shadows

Authors: Ryan J. Buchanan
Comments: 4 Pages. (Abstract added to Article by viXra Admin - Please conform!)

These notes were taken whilst thinking about the monotone-light factorization, which lead to the productive idea of a shadow category, or a certain kind of category with a preordered structure.
Category: Set Theory and Logic

[2] viXra:2307.0071 [pdf] submitted on 2023-07-13 01:41:33

Letter Theory, Creating and Describing Mathematical Axioms of a System for Letters which Creates Most Simplified Language with Provable Sentences

Authors: Iman Mosleh
Comments: 16 Pages.

This paper is a cross field work between theology, linguistics and mathematics (abstract algebra, topology, set theory, fractal geometry and number theory) which tries to establish a letter system to define word meanings by letter meanings and to restart mathematical theology on this planet which we think had been started by Abraham the prophet.We try to answer this question that can we create a meaning system which every alphabet letter has an specific meaning in, and when we combine them to create words we have a clear system to define every word meaning just by its letters meaning and order of that letters in the word?We will show that if we have a fractal system we can establish a letter system for it.The other question which i try to answer is that can we produce a letter system which provide us provable sentences?
Category: Set Theory and Logic

[1] viXra:2307.0040 [pdf] replaced on 2023-09-25 22:55:19

Any Formal System That Contains Sets Arithmetic and Rational Numbers is Inconsistent

Authors: Jim Rock
Comments: 1 Page.

Gӧdel proved that any formal system containing arithmetic is incomplete. We show that any such formal system is inconsistent. We establish a collection of nested sets of rational numbers in a descending hierarchy. The sets higher in the descending hierarchy contain element(s) that are not in the sets below them in the hierarchy. Given such a descending set hierarchy, it is easy to develop two arguments that contradict each other. The conclusion of Argument#2 is false. But, Argument#2 is a valid argument.
Category: Set Theory and Logic