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单词 ConsequenceOperatorIsDeterminedByItsFixedPoints
释义

consequence operator is determined by its fixed points


Theorem 1

Suppose that C1 and C2 are consequence operators on a set L and that,for every XL, it happens that C1(X)=X if and only if C2(X)=X. Then C1=C2.

Theorem 2

Suppose that C is a consequence operators on a set L. Define K={XLC(X)=X}. Then, for every XL, there exists a YKsuch that XY and, for every ZK such that XZ,one has YZ.

Theorem 3

Given a set L, suppose that K is a subset of L such that, for every XL, there exists a YK such that XY and, for every ZK such that XZ, one has YZ. Then there exists aconsequence operator C:P(L)P(L) such that C(X)=X if and only if XK.

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