特殊篇章玄宇宙计划原文序列部分章 (10-4)

candidates themselves. The concept of set is called upon for this purpose, AB) where the view is taken that a set is somethingobtainable from the integers (orsome other well-defined object) by iterated application of the operation “set

of” ([9]. p. 180). A special emphasis is put on the maximizing implications

of that concept, to the effect that axioms “stating the existence of still further

iterations of the operation set of",like “small” large cardinal hypotheses.

are regarded as fully legitimate candidates for new set-theoretic axioms.

[9].however,does not rule out the possibility that, beyond the concept of

set, there may be other motivations that succeed in indicating reasonable

strategics for extending ZFC. In fact it is conjectured that “there may exist

besides the ordinary axioms [...] other (hitherto unknown) axioms of set

theory which a more profound understanding of the concepts underlying

logic and mathematics would enable us to recognize as implied by these

concepts”([9]. p. 182). The suggestion is also made, in [10], that some

maximum property of the system of sets may be devised that is not directly

suggested by the concept of set, yet may work as a reasonable new axiom for

set theory ("[...] from an axiom in some sense opposite to this one [V=L]

the negation of Cantor's conjecture could perhaps be derived. I am thinking

of an axiom which [...] would state some maximum property of the system

of all sets […]”. [10]. p.478).

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