DefBinaryIntersection (3.54, Definition): Binary intersection

Standalone kernel entity record from 3. Set/Class-Theoretic Foundations (3.01–3.78) — View in Complete Entity Database (#DefBinaryIntersection) →

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DefBinaryIntersection (3.54) — Binary intersection

Morse-Kelley / Von Neumann-Bernays-Gödel class comprehension, sethood, ordinals, Dunaev pairs, cardinals, universes, and reflection.

Num Entity Database Record (Vertical Field Table)
3.54
Title Binary intersection #DefBinaryIntersection #label-binary-intersection
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{A} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{B} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{A} \href{../symbols/bininter-op.html}{\cap} \href{../symbols/variables.html}{B} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/eq-pred.html}{=} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{x} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{A} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/and-conn.html}{\land} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{x} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{B} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpBinInter
Scheme of Types 0(∀([A@Variable]:[Class@Type])∀([B@Variable]:[Class@Type])(([A@Class.Expression]∩[B@Class.Expression])={[x@Class.Expression]|([x@Class.Expression]∈[A@Class.Expression])∧([x@Class.Expression]∈[B@Class.Expression])}))
Verification Definitional (Kernel AST) · Standalone Entry (DefBinaryIntersection) → · (3.54) · #DefBinaryIntersection