Hereditary \(\mathrm{Hereditary}\) — Hereditary Class Predicate (Hereditary, AST Constructor: TpHereditary)
Unary predicate Hereditary(U) ⟷ ∀(x∈U)((𝒫(x) ∩ 𝒱) ⊆ U) asserting closure under subsets (Entry DefHereditaryClass (3.44)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
Hereditary
\(\mathrm{Hereditary}\)
|
| Category | Predicate Symbol (Unary Class Predicate) |
| SML AST Constructor | HP (TpHereditary of 'Class_EXP) [in datatype Truth_p, typetheory.ML:665] |
| Constructor Arguments | 1. Class U : Class |
| Metatype / Signature | Class → Bool |
| Binder Status | No — Unary Predicate Symbol |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{Hereditary} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | Hereditary(U) ⟷ ∀(x∈U)((𝒫(x) ∩ 𝒱) ⊆ U) |
| Related Symbols & Kernel Entries |