ThmOmegaInOrdinals (3.63, Theorem): ω is in the class of all ordinal numbers(=sets)

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

Formula Display:
Proof Trees:

ThmOmegaInOrdinals (3.63) — ω is in the class of all ordinal numbers(=sets)

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

Num Entity Database Record (Vertical Field Table)
3.63
Title ω is in the class of all ordinal numbers(=sets) #ThmOmegaInOrdinals #label-is-in-the-class-of-all-ordinal-numbers-sets
Classification Theorem
Formula
0(ω∈On)
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/omega-const.html}{\omega} \href{../symbols/in-pred.html}{\in} \href{../symbols/on-const.html}{\mathbf{On}} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpOn
Scheme of Types 0(ω∈On)
Verification Verified (Kernel) · Standalone Entry (ThmOmegaInOrdinals) → · (3.63) · #ThmOmegaInOrdinals