DefIsSet (3.02, Definition): “Is a set” predicate

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

Formula Display:
Proof Trees:

DefIsSet (3.02) — “Is a set” predicate

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

Num Entity Database Record (Vertical Field Table)
3.02
Title “Is a set” predicate #DefIsSet #label-is-a-set-predicate
Classification Definition
Formula
0\(\href{../symbols/delimiters-brackets.html}{(} \href{../symbols/forall-binder.html}{\forall} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/set-pred.html}{\mathsf{set}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/iff-conn.html}{\longleftrightarrow} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/exists-binder.html}{\exists} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{Y} \href{../symbols/typing-colon.html}{:} \href{../symbols/class-type.html}{\mathsf{Class}} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{(} \href{../symbols/variables.html}{X} \href{../symbols/in-pred.html}{\in} \href{../symbols/variables.html}{Y} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \href{../symbols/delimiters-brackets.html}{)} \)
SML Kernel AST PSetDef_prf
Scheme of Types 0(∀([X@Variable]:[Class@Type])(([X@Class.Expression] set)⟷(∃([Y@Variable]:[Class@Type])([X@Class.Expression]∈[Y@Class.Expression]))))
Verification Definitional (Kernel AST) · Standalone Entry (DefIsSet) → · (3.02) · #DefIsSet