集合矩阵理论作为Zermelo-Fraenkel集合理论的物理动机推广

IF 0.3 3区哲学 Q1 Arts and Humanities

Logique et Analyse Pub Date : 2012-02-09 DOI:10.2143/LEA.225.0.3011356

M. Cabbolet, H. Swart

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引用次数: 3

摘要

最近，基本过程理论(EPT)已经发展成为一套基本原理，可能是物质和反物质引力排斥的基础。本文提出了集合矩阵理论(SMT)作为EPT形式化的数学框架的基础:即，使用Zermelo-Fraenkel集合理论(ZF)是令人反感的。SMT是ZF的推广:而ZF只使用集合作为原始对象，在SMT的框架中，具有集值项的矩阵是自属对象，具有1 1集合矩阵[x]与集合x相同。证明了每一个可以在ZF中构造的集合也可以在SMT中构造:作为数学基础，SMT并不弱于ZF。此外，还表明SMT比ZF更适合于预期的物理应用。结论是，与ZF相反，SMT可以作为由EPT决定的物理框架的数学逻辑基础。

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Set matrix theory as a physically motivated generalization of Zermelo-Fraenkel set theory

Recently, the Elementary Process Theory (EPT) has been developed as a set of fundamental principles that might underlie a gravitational repulsion of matter and antimatter. This paper presents set matrix theory (SMT) as the foundation of the mathematicallogical framework in which the EPT has been formalized: it is, namely, objectionable to use Zermelo-Fraenkel set theory (ZF) as such. SMT is a generalization of ZF: whereas ZF uses only sets as primitive objects, in the framework of SMT nite matrices with set-valued entries are objects sui generis, with a 1 1 set matrix [x] being identical to the set x. It is proved that every set that can be constructed in ZF can also be constructed in SMT: as a mathematical foundation, SMT is thus not weaker than ZF. In addition, it is shown that SMT is more suitable than ZF for the intended application to physics. The conclusion is that SMT, contrary to ZF, is acceptable as the mathematical-logical foundation of the framework for physics that is determined by the EPT.

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来源期刊

Logique et Analyse PHILOSOPHY-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Logique et Analyse is the continuation of Bulletin Intérieur, which was published from 1954 on by the Belgian National Centre for Logical Investigation, and intended originally only as an internal publication of results for its members and collaborators. Since the start of the new series, in 1958, however, the journal has been open to external submissions (and subscriptions). Logique et Analyse itself subscribes to no particular logical or philosophical doctrine, and so is open to articles from all points of view, provided only that they concern the designated subject matter of the journal.