DefCardinality (3.41, Definition): Class cardinality

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

Formula Display:
Proof Trees:

DefCardinality (3.41) — Class cardinality

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

Num Entity Database Record (Vertical Field Table)
3.41
Title Class cardinality #DefCardinality #label-class-cardinality
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{K} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/card-op.html}{ \mid } \href{../symbols/variables.html}{K} \href{../symbols/card-op.html}{ \mid } \href{../symbols/eq-pred.html}{=} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/on-const.html}{\mathbf{On}} \href{../symbols/bininter-op.html}{\cap} \href{../symbols/biginter-op.html}{\bigcap} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{a} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{a} \href{../symbols/in-pred.html}{\in} \href{../symbols/on-const.html}{\mathbf{On}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/and-conn.html}{\land} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{K} ≼\href{../symbols/variables.html}{a} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpCard
Scheme of Types 0(∀([K@Variable]:[Class@Type])(|[K@Class.Expression]|=(On∩⋂{[a@Class.Expression]|([a@Class.Expression]∈On)∧([K@Class.Expression]≼[a@Class.Expression])})))
Verification Definitional (Kernel AST) · Standalone Entry (DefCardinality) → · (3.41) · #DefCardinality