universe \(\mathrm{universe}\) — Grothendieck-Tarski Universe Predicate (universe, AST Constructor: TpUniverse)
Unary predicate (U is a universe) ⟷ (Tr(U) ∧ Hereditary(U) ∧ Powerful(U) ∧ Pairful(U) ∧ Tight(U)) (Entries RulClassComprehension (3.01)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
universe
\(\mathrm{universe}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpUniverse of 'Class_EXP) [in datatype Truth_p, typetheory.ML:663] |
| Constructor Arguments | 1. Class U : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol (Grothendieck-Tarski Universe) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{universe} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | (U is a universe) ⟷ (Tr(U) ∧ Hereditary(U) ∧ Powerful(U) ∧ Pairful(U) ∧ Tight(U)) |
| Related Symbols & Kernel Entries |