ThmOmegaCardinal (3.65, Theorem): ω is cardinal

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

Formula Display:
Proof Trees:

ThmOmegaCardinal (3.65) — ω is cardinal

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

Num Entity Database Record (Vertical Field Table)
3.65
Title ω is cardinal #ThmOmegaCardinal #label-is-cardinal
Classification Theorem
Formula
0\(\href{../symbols/card-pred.html}{\mathrm{Card}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/omega-const.html}{\omega} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST TpCard
Scheme of Types 0Card(ω)
Verification Verified (Kernel) · Standalone Entry (ThmOmegaCardinal) → · (3.65) · #ThmOmegaCardinal