Set Theory and Logic

2011 Submissions

[4] viXra:2011.0160 [pdf] submitted on 2020-11-22 10:57:30

There Are Questions with Hidden Answer, But Without a Way to Find the Answer

Authors: Dmitri Martila
Comments: 3 Pages. Rejected by many top journals without review

Re-proof of Gödel incompleteness theorem. I use no mathematical expressions.
Category: Set Theory and Logic

[3] viXra:2011.0014 [pdf] replaced on 2021-03-25 03:56:23

Cantor Diagonal Argument

Authors: Antonio Leon
Comments: 9 Pages.

This paper proves a result on the decimal expansion of the rational numbers in the open rational interval (0, 1), which is subsequently used to discuss a reordering of the rows of a table T that is assumed to contain all rational numbers within (0, 1), in such a way that the diagonal of the reordered table T could be a rational number from which different rational antidiagonals (elements of (0, 1) that cannot be in T ) could be defined. If that were the case, and for the same reason as in Cantor’s diagonal argument, the open rational interval (0, 1) would be non-denumerable, and we would have a contradiction in set theory, because Cantor also proved the set of rational numbers is denumerable.
Category: Set Theory and Logic

[2] viXra:2011.0013 [pdf] replaced on 2020-12-10 12:36:06

Hilbert Machine

Authors: Antonio Leon
Comments: 7 Pages.

Inspired by the emblematic Hilbert Hotel, Hilbert machine is a conceptual super-machine whose functioning questions the consistency of the actual infinity hypothesis subsumed into the Axiom of Infinity.
Category: Set Theory and Logic

[1] viXra:2011.0012 [pdf] replaced on 2020-12-01 05:28:53

Zeno Dichotomies

Authors: Antonio Leon
Comments: 10 Pages.

This chapter introduces a formalized version of Zeno’s Dichotomy in its two variants (here referred to as Dichotomy I and II) based on the discreteness and separation of ω-order (Dichotomy I) and of ω∗-order (Dichotomy II) defined below in this section. Each of these formalized versions leads to a contradiction pointing to the inconsistency of the hypothesis of the actual infinity.
Category: Set Theory and Logic