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Eine Note zum System PC (1977)

Christian, Curt

Springer

Monatshefte für Mathematik 83 (1977), S. 191-200

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ISSN: 1436-5081

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Corresponding to a graduation of the comprehension predicateC there arise two systems PC1 and PC2. PC1 represents constructive mathematics whereas PC2 as a restricted enlargement of PC1 enables one to deal with full set theory. Unnatural definitions likeKuratowski's ordered pair and identification of 0 and $$\not 0$$ are avoided. In PC1 the postulate introduced for ordered pairs holds not only for sets but for classes generally. The comprehension condition in PC1 implicitly contains a set axiom for at most denumerable calsses and for ordered pairs. By introduction of the concept “ordered self-pair” the real numbers are interpreted as self-pairs of (non denumerable) equivalence classes of concentrated ratioal sequences and they can be shown to be sets in PC1.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01541635

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