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- Kunen's_inconsistency_theorem abstract "In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen (1971), shows that several plausible large cardinal axioms are inconsistent with the axiom of choice.Some consequences of Kunen's theorem are:There is no non-trivial elementary embedding of the universe V into itself. In other words, there is no Reinhardt cardinal.If j is an elementary embedding of the universe V into an inner model M, and λ is the smallest fixed point of j above the critical point κ of j, then M does not contain the set j "λ (the image of j restricted to λ).There is no ω-huge cardinal.There is no non-trivial elementary embedding of Vλ+2 into itself.It is not known if Kunen's theorem still holds in ZF (ZFC without the axiom of choice), though Suzuki (1999) showed that there is no definable elementary embedding from V into V. That is there is no formula J in the language of set theory such that for some parameter p∈V for all sets x∈V and y∈V: Kunen used Morse–Kelley set theory in his proof. If the proof is re-written to use ZFC, then one must add the assumption that replacement holds for formulas involving j. Otherwise one could not even show that j "λ exists as a set. The forbidden set j "λ is crucial to the proof. The proof first shows that it cannot be in M. The other parts of the theorem are derived from that.".
- Kunen's_inconsistency_theorem wikiPageID "25426123".
- Kunen's_inconsistency_theorem wikiPageRevisionID "547157972".
- Kunen's_inconsistency_theorem authorlink "Kenneth Kunen".
- Kunen's_inconsistency_theorem first "Kenneth".
- Kunen's_inconsistency_theorem hasPhotoCollection Kunen's_inconsistency_theorem.
- Kunen's_inconsistency_theorem last "Kunen".
- Kunen's_inconsistency_theorem year "1971".
- Kunen's_inconsistency_theorem subject Category:Large_cardinals.
- Kunen's_inconsistency_theorem type Bishop109857200.
- Kunen's_inconsistency_theorem type Cardinal109894143.
- Kunen's_inconsistency_theorem type CausalAgent100007347.
- Kunen's_inconsistency_theorem type Clergyman109927451.
- Kunen's_inconsistency_theorem type LargeCardinals.
- Kunen's_inconsistency_theorem type Leader109623038.
- Kunen's_inconsistency_theorem type LivingThing100004258.
- Kunen's_inconsistency_theorem type Object100002684.
- Kunen's_inconsistency_theorem type Organism100004475.
- Kunen's_inconsistency_theorem type Person100007846.
- Kunen's_inconsistency_theorem type PhysicalEntity100001930.
- Kunen's_inconsistency_theorem type Priest110470779.
- Kunen's_inconsistency_theorem type SpiritualLeader109505153.
- Kunen's_inconsistency_theorem type Whole100003553.
- Kunen's_inconsistency_theorem type YagoLegalActor.
- Kunen's_inconsistency_theorem type YagoLegalActorGeo.
- Kunen's_inconsistency_theorem comment "In set theory, a branch of mathematics, Kunen's inconsistency theorem, proved by Kenneth Kunen (1971), shows that several plausible large cardinal axioms are inconsistent with the axiom of choice.Some consequences of Kunen's theorem are:There is no non-trivial elementary embedding of the universe V into itself.".
- Kunen's_inconsistency_theorem label "Kunen's inconsistency theorem".
- Kunen's_inconsistency_theorem sameAs m.09k5p6_.
- Kunen's_inconsistency_theorem sameAs Q6444407.
- Kunen's_inconsistency_theorem sameAs Q6444407.
- Kunen's_inconsistency_theorem sameAs Kunen's_inconsistency_theorem.
- Kunen's_inconsistency_theorem wasDerivedFrom Kunen's_inconsistency_theorem?oldid=547157972.
- Kunen's_inconsistency_theorem isPrimaryTopicOf Kunen's_inconsistency_theorem.