By G. B Keene

ISBN-10: 0486155005

ISBN-13: 9780486155005

This textual content unites the logical and philosophical features of set conception in a way intelligible either to mathematicians with no education in formal good judgment and to logicians and not using a mathematical history. It combines an undemanding point of therapy with the top attainable measure of logical rigor and precision. 1961 variation.

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

**Example text**

By its means elegant and powerful logical calculi can be set up for the purpose of formalizing a scientific theory. But familiarity with the techniques involved in setting up these logical calculi is not essential to an understanding of the present text. All that is required is an understanding of the meaning and interrelation of the following symbols: ∼, , v, ⊃, ≡, (x)φ, (∃x)φ, ε All of them translate straightforwardly into a familiar word or phrase of ordinary speech. But they are not mere shorthand symbols.

C. Kleene, for his approval of my adaptation of material published in that Journal. Exeter G. B. K. 1. Introduction THE symbolism of elementary logic is both simple and efficient. By its means elegant and powerful logical calculi can be set up for the purpose of formalizing a scientific theory. But familiarity with the techniques involved in setting up these logical calculi is not essential to an understanding of the present text. All that is required is an understanding of the meaning and interrelation of the following symbols: ∼, , v, ⊃, ≡, (x)φ, (∃x)φ, ε All of them translate straightforwardly into a familiar word or phrase of ordinary speech.

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.

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

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