Symbol Reference: Card — Cardinal Class Predicate (Card, AST Constructor: TpCard)

Personal Symbol Reference Page in MKTD1 & MKTD2 (Morse-Kelley + Tarski + Dunaev) — All Personal Symbol Pages → | Full Symbol Registry →

Formula Display:
Proof Trees:

Card \(\mathrm{Card}\) — Cardinal Class Predicate (Card, AST Constructor: TpCard)

Unary predicate Card(K) ⟷ ∃(C:Class)(|C| = K) asserting that K is the cardinality of some class (Entry ThmOmegaInOrdinals (3.63)).

Field Mathematical & Kernel Specification (MKTD1 / MKTD2)
Symbol
Card
\(\mathrm{Card}\)
Category Predicate Symbol (Unary Class Predicate)
SML AST Constructor HP (TpCard of 'Class_EXP) [in datatype Truth_p, typetheory.ML:671]
Constructor Arguments 1. Class K : Class
Metatype / Signature Class → Bool
Binder Status No — Unary Predicate Symbol (Cardinal Class)
Defining Kernel Entries (ML Labels) See Related Symbols & Kernel Entries below.
LaTeX Form \mathrm{Card}
How to Understand It

SML AST Constructor: HP (TpCard of 'Class_EXP) in Truth_p (typetheory.ML:671). Takes one class argument K : Class.

Canonical Law / Usage Card(K) ⟷ ∃(C:Class)(|C| = K)
Related Symbols & Kernel Entries