Suppes Axiomatic Set Theory Pdf May 2026

Denoted ( \bigcup A ). For any set A, there exists a set whose members are exactly all subsets of A. [ \forall A \exists P \forall x [x \in P \leftrightarrow x \subseteq A] ]

Proof : Let ( A ) and ( B ) be sets. By Pairing, ( A, B ) is a set. By Union, ( \bigcup A, B ) is a set. But ( \bigcup A, B = A \cup B ). QED. suppes axiomatic set theory pdf

Denoted ( \emptyset ). For any sets a, b, there exists a set whose members are exactly a and b. [ \forall a \forall b \exists x \forall y (y \in x \leftrightarrow y = a \lor y = b) ] Denoted ( \bigcup A )

: The union of two sets is a set.