On \(\mathrm{On}\) — Class of All Ordinals Constant (On, AST Constructor: CpOn)
0-ary class constant On = {x | Ord(x)} denoting the proper class of all ordinal sets (Entry DefClassOfOrdinals (3.17)).
| Field | Mathematical & Kernel Specification (MKTD1 / MKTD2) |
|---|---|
| Symbol |
On
\(\mathrm{On}\)
|
| Category | Functional Symbol (0-ary Class Constant) |
| SML AST Constructor | HC CpOn [in datatype Class_p, typetheory.ML:557] |
| Constructor Arguments | 0-ary constant (no arguments) |
| Metatype / Signature | Class |
| Binder Status | No — Defined 0-ary Functional Symbol (Class of All Ordinals) |
| Defining Kernel Entries (ML Labels) | See Related Symbols & Kernel Entries below. |
| LaTeX Form | \mathrm{On} |
| How to Understand It | SML AST Constructor: |
| Canonical Law / Usage | On = {x | Ord(x)} |
| Related Symbols & Kernel Entries |