Titlebook: Introduction to Axiomatic Set Theory; Gaisi Takeuti,Wilson M. Zaring Textbook 19711st edition Springer-Verlag Berlin Heidelberg 1971 arith

效果

https://doi.org/10.1007/978-1-4684-9915-5arithmetic; axiom of choice; function; logic; ordinal; set; set theory

Absenteeism

Language and Logic,The language of our theory consists of

adumbrate

The Elementary Properties of Classes,In this section we will introduce certain properties of classes with which the reader is already 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.

APNEA

Ordinal Arithmetic,In Section 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 ∈-relation. As a well ordered set . + 1 has an initial segment . and its “terminal” segment beginning with . consists of just a single element, namely ..

神经

Cardinal Numbers,The equivalence of sets is basic to the theory of cardinal numbers. Two sets are equivalent, or equipollent, provided there exists a one-to-one correspondence between them.

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Gratulate

,Cohen’s Method,In proving that the AC and the GCH are consistent with ZF Gödel used the so called method of internal models. From the assumption that the universe . is a model of ZF Gödel prescribed a method for producing a submodel . that is also a model of ., AC and GCH. This submodel is defined as the class of all sets having a certain property i.e. ..