By G. B Keene

ISBN-10: 0486155005

ISBN-13: 9780486155005

This textual content unites the logical and philosophical features of set concept in a fashion intelligible either to mathematicians with no education in formal common sense and to logicians with out a mathematical historical past. It combines an simple point of remedy with the top attainable measure of logical rigor and precision. 1961 variation.

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**Extra info for Abstract Sets and Finite Ordinals. An Introduction to the Study of Set Theory**

**Sample text**

The propositional function is the most important among the various types of formula with which we shall be concerned in Part II. g. g. (II) above). In this connection we shall, for convenience, use the phrase “formula which represents a true (false) proposition” in the following way. A formula may represent a true (false) proposition either directly (as in the case of a symbolized proposition), or indirectly (as in the case of a formula containing variables which is assumed, for the sake of a particular argument, to give rise to some particular but unspecified true (false) proposition, by a suitable assignment of values to the variables).

And suppose that the result of omitting from a class of normal (m+1)-tuplet all (m+1)-tuplets whose first two members differ, is a class. Now, by the first of these suppositions, we can obtain from the required class of normal (k+j)-tuplets. If, on the other hand, ψ and φ had had at least one argument in common, we could obtain, in the same way, a class of normal (k+j)-tuplets each of which had at least two identical members. By the second supposition, above, we could reorder each of the elements of this class so that in each case the first two members were identical.

16, p. 27). (c1) Let the class so defined (the domain of a class of pairs) be: A or:/A/ (cf. Fig. 17, p. 28). (c2) Let the class so defined (the converse class of a class of pairs) be: ˘A or: ˘/A/(cf. Fig. 18, p. 29). (c3) Let the class so defined (the coupling-to-the-left of a class of pairs) be: →A or: →/A/. Note: From the classes admitted by AxIII we may construct other classes as required. For example, we can construct the class “mem1 USt” out of the classes mem1A and USt, as follows: In our exposition of the system we shall, however, take such moves as these as understood, and in such a case as this, proceed direct to line (4) from the axioms.

### Abstract Sets and Finite Ordinals. An Introduction to the Study of Set Theory by G. B Keene

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