ThmOmegaOrdinal (3.62, Theorem): ω is ordinal

Standalone kernel entity record from 3. Set/Class-Theoretic Foundations (3.01–3.78) — View in Complete Entity Database (#ThmOmegaOrdinal) →

Formula Display:
Proof Trees:

ThmOmegaOrdinal (3.62) — ω is ordinal

Morse-Kelley / Von Neumann-Bernays-Gödel class comprehension, sethood, ordinals, Dunaev pairs, cardinals, universes, and reflection.

Num Entity Database Record (Vertical Field Table)
3.62
Title ω is ordinal #ThmOmegaOrdinal #label-is-ordinal
Classification Theorem
Formula
0\(\href{../symbols/ord-pred.html}{\mathrm{Ord}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/omega-const.html}{\omega} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpOrd
Scheme of Types 0Ord(ω)
Verification Verified (Kernel) · Standalone Entry (ThmOmegaOrdinal) → · (3.62) · #ThmOmegaOrdinal