Set Theory and Logic

2405 Submissions

[2] viXra:2405.0163 [pdf] replaced on 2025-08-26 01:36:46

Beyond Gödel

Authors: Jim Rock
Comments: 2 Pages.

In 1930 Gödel wrote a landmark paper showing that in any formal system there will always bestatements that cannot be proven. But the deficiency of formal systems goes much deeper. The same logically valid statement can be used in conjunction with two different sets simultaneously proving a true statement and a false statement. This result is profound. It explains why people can use the same sound argument to prove two contradictory statements. It is no wonder the most lucid arguments still sometimes result in hung juries and earnest people can disagree on the most fundamental issues. Truth is a much deeper concept than logical validity.
Category: Set Theory and Logic

[1] viXra:2405.0143 [pdf] replaced on 2026-06-09 18:47:30

About Countability Sets

Authors: Tomasz Soltysiak
Comments: 9 Pages.

A refutation of Cantor's diagonal argument. A proof of the equality of the number of elements in the sets of natural and real numbers. A refutation of Cantor's power set theorem for infinite sets. A proof of the equality of the number of elements in an infinite set and its power set. Geometric proof. The relationship between infinity and the number zero. The theorem on the countability of all sets.
Category: Set Theory and Logic