Symbol Reference: |C| — Cardinality Functional Symbol (|C|, AST Constructor: CpCard)

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|C| \(|C|\) — Cardinality Functional Symbol (|C|, AST Constructor: CpCard)

Unary functional symbol |C| = ⋂{w | (w∈On) ∧ (C ⪯ w)} mapping a class C to its initial ordinal cardinal (Entry DefCardinality (3.41)).

Field Mathematical & Kernel Specification (MKTD1 / MKTD2)
Symbol
|C|
\(|C|\)
Category Functional Symbol (Unary Class Operator)
SML AST Constructor HC (CpCard of 'Class_EXP) [in datatype Class_p, typetheory.ML:571]
Constructor Arguments 1. Class C : Class
Metatype / Signature Class → Class
Binder Status No — Unary Mixfix Functional Symbol (Initial Ordinal Cardinality |C|)
Defining Kernel Entries (ML Labels) See Related Symbols & Kernel Entries below.
LaTeX Form |C|
How to Understand It

SML AST Constructor: HC (CpCard of 'Class_EXP) in Class_p (typetheory.ML:571). Takes one class argument C : Class. Vertical bars |C| outside comprehension braces resolve to this functional symbol.

Canonical Law / Usage |C| = ⋂{w | (w ∈ On) ∧ (C ⪯ w)}
Related Symbols & Kernel Entries