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| viXra.org > Set Theory and Logic > 2302 |
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[5] viXra:2302.0145 [pdf] submitted on 2023-02-28 01:44:54
Authors: Jim Rock
Comments: 1 Page.
Here two contradictory arguments are defended. They can be developed in any formal system containing sets, arithmetic, and relations between the rational numbers.
Category: Set Theory and Logic
[4] viXra:2302.0113 [pdf] submitted on 2023-02-23 01:44:03
Authors: Yanhong Yang
Comments: 3 Pages.
The existence of the premise: S=1，Then there is at least one P Problem(Computer-table problems)equal to NP problem (The solution is a computer-verifiable problem) then: P←→NP(P=NP). Thus, For all the class P and class NP problems，There are P=NP，also have P≠NP.
Category: Set Theory and Logic
[3] viXra:2302.0092 [pdf] submitted on 2023-02-20 03:47:09
Authors: Jincheng Zhang
Comments: 18 Pages.
For a long time, there is a "diagonal method of proof" dominating the mathematics field; with it, Russel finds the paradox of set theory; with it, Cantor proves that "the power set of natural numbers is uncountable" and " the set of real numbers is uncountable"; with it , Gödel proves that " natural number system PA is incomplete"; with it , Turning proves that " halting problem" is undecidable and proves that " there is non-recursive sets on sets of natural numbers" in recursion theory and so on; proofs of these significant propositions all apply the same mathematic method which is praised as " a golden diagonal". On the basis of analyzing paradoxes, the paper finds that paradoxes are unclosed terms on closed calculus (that is extra-field term). Classical logic system cannot handle such extra-field terms, so it is transformed to the logic systems SL, SK that may handle unclosed calculus. It can be found that "diagonal proof method" is to construct paradoxes in nature through further analysis, and it is an unclosed proof method, which can prove that real numbers constructed by Cantor’s "diagonal proof method are extra-field terms which will not affect count-ability of sets of real numbers; The Gödel’s undeterminable proposition is an extra-field term, which will not affect completeness of system PA. The undeterminable Turing machine in the Turing halt problem is also an extra-field term. So, the proof that real number is uncountable is wrong; the proof of Gödel’s incomplete theorem and diagonal method of proof, all of them are wrong, should be completely corrected.
Category: Set Theory and Logic
[2] viXra:2302.0091 [pdf] submitted on 2023-02-20 01:36:24
Authors: Jincheng Zhang
Comments: 13 Pages.
There exists a Gödel number for each formula of the system N of natural numbers. The Gödel undecidable proposition, which is also a formula of the system N, also exists a Gödel number p; at the same time, the Gödel undecidable proposition is a self-referential proposition u([p]) substituted into its own Gödel number, and the self-referential proposition u([p]) Gödel number is also p, i.e., there is, u([p])=p. It can be This equation has no solution.The traditional view is that the Gödel undecidable proposition u([p]) is a closed formula and is a natural number proposition; we here transform the Gödel self-referential proposition into a self-referential equation and find that this equation has no solution and the Gödel undecidable proposition u([p]) is not a natural number proposition. u([p]) is an unclosed term (out-of-domain term) that evolves on the set of natural numbers and u([p]) is not a closed formula.
Category: Set Theory and Logic
[1] viXra:2302.0039 [pdf] submitted on 2023-02-10 02:15:24
Authors: Ryan J. Buchanan
Comments: 6 Pages.
This paper includes a formulation of extended modal realism and a theorem concerning its equivalence with a certain mathematical universe.
Category: Set Theory and Logic
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