Set Theory and Logic

2106 Submissions

[5] viXra:2106.0160 [pdf] submitted on 2021-06-28 17:45:34

A Rigorous Examination on Cantors Diagonal Argument

Authors: Hongyi Li
Comments: 5 Pages.

It was proved in this paper that diagonal argument actually only proves that the real numbers can not be listed as complete, which has nothing to do with if the real numbers are countable or not. The confusion of the two different concepts - Countable and “complete listing” - is the reason why the diagonal argument fails. It was proved that real numbers are countable.
Category: Set Theory and Logic

[4] viXra:2106.0159 [pdf] replaced on 2021-10-08 23:53:33

The Fog Covering Cantor's Paradise: Some Paradoxes on Infinity and Continuum

Authors: Ke Zhang
Comments: 19 pages English + 19 pages Chinese. Mail: alspa@163.com

We challenge Georg Cantor's theory about infinity. By attacking the concept of “countable/uncountable” and diagonal argument, we reveal the uncertainty, which is obscured by the lack of clarity. The problem arises from the basic understandings of infinity and continuum. We perform many thought experiments to refute current standard views. The results support the opinion that no potential infinity leads to an actual infinity, nor is there any continuum composed of indivisibles statically, nor is Cantor's theory consistent in itself.
Category: Set Theory and Logic

[3] viXra:2106.0138 [pdf] submitted on 2021-06-23 05:33:29

A New Approach to Set Theory, Version 1.5

Authors: Thomas Limberg
Comments: 9 pages; language: German; for receiving the program "Demonstration of the Limberg calculus", version 1.2, email me!

We introduce a simple logical calculus called Limberg Calculus and two attached derivation sequences. The derivation sequences contain a proof, that empty and universal set exist (under the Limberg Calculus).
Category: Set Theory and Logic

[2] viXra:2106.0067 [pdf] submitted on 2021-06-10 23:51:30

Infinity and Numerical Magic

Authors: Antonio Leon
Comments: 7 Pages.

This chapter analyzes a supertask that makes it disappear numbers from a table that contains the list of natural numbers in their natural order of precedence.
Category: Set Theory and Logic

[1] viXra:2106.0043 [pdf] submitted on 2021-06-07 19:50:06

A Critique of Self-Reference: What Gödel Theorem Really Proves

Authors: Antonio Leon
Comments: 9 Pages.

This article introduces a new perspective for the analysis of self-referential sentences, and proves the conditions under which they are inconsistent. The Liar Paradox, Grelling-Nelson Paradox, Russell's Predicate Paradox, Russell's Set Paradox and Richard Paradox are proved to meet such conditions. The same is proved of the ordinary language interpretation of Gödel's undecidable formula if the corresponding formal calculus is complete. In consequence, Gödel's Theorem VI only holds if that calculus is not complete, which makes the theorem unnecessary. All proofs and arguments in this article are developed within the framework of a simplified system of ordinary logic also defined in this paper.
Category: Set Theory and Logic