Titlebook: Introduction to Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 1982Latest edition Springer-Verlag New York Inc. 1982 Cardin

牙齿

合乎习俗

Silver Machines,y simply as a means to an end. That, however, is not at all the case. Gödel held his discovery of constructible sets, and his proof that the class of constructible sets, ., is a model of ZFC, to be by itself, one of his major achievements. His confidence in the importance of the notion of constructi

细菌等

使人烦燥

The Elementary Properties of Classes,In this chapter we will introduce certain properties of classes with which the reader is probably familiar. The immediate consequences of the definitions are for the most part elementary and easily proved; consequently they will be left to the reader as exercises.

STAT

Ordinal Arithmetic,In Chapter 7 we defined . + 1 to be . ∪ {.}. We proved that . + 1 is an ordinal, that is, . + 1 is a transitive set that is well ordered by the e-relation. As a well-ordered set . + 1 has an initial segment . and its “terminal” segment beginning with . consists of just a single element, namely ..

Anthropoid

dura-mater

信徒

蚊帐

,The Gödel Model,In Chapter 7 we defined a relation . on On.. We proved that . well orders On. and, with respect to ., initial segments of On. are sets. Consequently there is an order isomorphism . such that ..

ABYSS