DefClassOfOrdinals (3.17, Definition): Class of all ordinal sets(ordinal numbers)

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

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DefClassOfOrdinals (3.17) — Class of all ordinal sets(ordinal numbers)

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

Num Entity Database Record (Vertical Field Table)
3.17
Title Class of all ordinal sets(ordinal numbers) #DefClassOfOrdinals #label-class-of-all-ordinal-sets-ordinal-numbers
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/on-const.html}{\mathbf{On}} \href{../symbols/eq-pred.html}{=} \href{../symbols/class-comprehension.html}{\{} \href{../symbols/variables.html}{w} \href{../symbols/class-comprehension.html}{ \mid } \href{../symbols/ord-pred.html}{\mathrm{Ord}} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{w} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/class-comprehension.html}{\}} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST CpOn
Scheme of Types 0(On={[w@Class.Expression]|Ord([w@Class.Expression])})
Verification Definitional (Kernel AST) · Standalone Entry (DefClassOfOrdinals) → · (3.17) · #DefClassOfOrdinals