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Single Idea 10537

[filed under theme 4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST ]

Full Idea

A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}.

Gist of Idea

The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}}

Source

Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)

Book Ref

Dummett,Michael: 'Frege Philosophy of Language' [Duckworth 1981], p.477

The 4 ideas with the same theme [useful simple theorems derived within set theory]:

13444 Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
18098 Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
10537 The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
9680 The empty set Φ is a subset of every set (including itself) [Priest,G]