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| viXra.org > Set Theory and Logic > 2305 |
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[4] viXra:2305.0128 [pdf] submitted on 2023-05-19 01:08:18
Authors: Robert Lloyd Jackson
Comments: 1 Page.
This paper defines the union and intersection of multiple sets.
Category: Set Theory and Logic
[3] viXra:2305.0060 [pdf] submitted on 2023-05-06 14:07:39
Authors: W. Mückenheim
Comments: 1 Page.
Shortest Proof of Dark Numbers
Category: Set Theory and Logic
[2] viXra:2305.0041 [pdf] submitted on 2023-05-06 00:43:19
Authors: Jincheng Zhang
Comments: 10 Pages.
:In this paper, the cardinal number problem is discussed separately in the axiom systems for set theory SZF+ and SZF-. It can be proved that:ordinal numbers and cardinal numbers are unified. There is no uncountable cardinal number; in Cantor’s set theory, definitions, theorems and propositions based on uncountable cardinal numbers and ordinal numbers are all false. In fact, Cantor’s continuum hypothesis is the cardinal number of a set of natural numbers, and whether there are other cardinal numbers between cardinal numbers of set of natural numbers |N| and cardinal numbers of power set |P (N)|, different interpretations are given in different axiom systems.
Category: Set Theory and Logic
[1] viXra:2305.0007 [pdf] replaced on 2023-05-05 21:40:37
Authors: Forrest C. Taylor
Comments: 100 Pages. CC BY-NC-ND 4.0 international license
A dependent type theory is proposed as the foundation of mathematics. The formalism preserves the structure of mathematical thought, making it natural to use. The logical calculus of the type theory is proved to be syntactically complete. Therefore it does not suffer from the limitations imposed by Gödel’s incompleteness theorems. In particular, the concept of mathematical truth can be defined in terms of provability.
Category: Set Theory and Logic
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