axiom of regularity वाक्य
उदाहरण वाक्य
मोबाइल
- The axiom of regularity is of a restrictive nature as well.
- Sets are well-founded if the axiom of Regularity is assumed.
- The axioms do not include the Axiom of regularity and Axiom of replacement.
- :See our article at Axiom of regularity.
- The axiom of regularity as it is normally stated implies LEM, whereas the form of set induction does not.
- The axiom of regularity was introduced by; it was adopted in a formulation closer to the one found in contemporary textbooks by.
- The axiom of regularity was also shown to be independent from the other axioms of ZF ( C ), assuming they are consistent.
- The axiom of regularity, which is one of the axioms of Zermelo Fraenkel set theory, asserts that all sets are well-founded.
- In addition to omitting the axiom of regularity, non-standard set theories have indeed postulated the existence of sets that are elements of themselves.
- The hereditarily finite sets, V ?, satisfy the axiom of regularity ( and all other axioms of ZFC except the axiom of infinity ).
- Using non-well-founded models that satisfy each axiom of ZFC except the axiom of regularity, that axiom is independent of the other ZFC axioms.
- Quine atoms cannot exist in systems of set theory that include the axiom of regularity, but they can exist in non-well-founded set theory.
- Note that saying that the membership relation of some model of ZF is well-founded is stronger than saying that the axiom of regularity is true in the model.
- It can be carried out in Zermelo & ndash; Fraenkel set theory, without using the axiom of choice, but making essential use of the axiom of regularity.
- This principle, sometimes called the "'axiom of induction "'( in set theory ), is equivalent to the axiom of regularity given the other well-founded induction.
- Appending this schema, as well as the axiom of regularity ( first proposed by Dimitry Mirimanoff in 1917 ), to Zermelo set theory yields the theory denoted by "'ZF " '.
- So " M " satisfies the axiom of regularity ( it is " internally " well-founded ) but it is not well-founded and the collapse lemma does not apply to it.
- The axiom of induction in KP is stronger than the usual axiom of regularity ( which amounts to applying induction to the complement of a set ( the class of all sets not in the given set ) ).
- Given the other axioms of Zermelo Fraenkel set theory, the axiom of regularity is equivalent to the intuitionistic theories ( ones that do not accept the law of the excluded middle ), where the two axioms are not equivalent.
- ZF set theory with the axiom of regularity removed cannot prove that any non-well-founded sets exist ( or rather, this would mean ZF is inconsistent ), but it is compatible with the existence of Quine atoms.
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