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Prenormality of ideals and completeness of their quotient algebras

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Morawiec A., Węglorz B.

Colloquium Mathematicum

1993

tom 64

nr 1

19-27

It is well known that if a nontrivial ideal ℑ on κ is normal, its quotient Boolean algebra P(κ)/ℑ is $κ^+$-complete. It is also known that such completeness of the quotient does not characterize normality, since P(κ)/ℑ turns out to be $κ^+$-complete whenever ℑ is prenormal, i.e. whenever there exists a minimal ℑ-measurable function in $^{κ}κ$. Recently, it has been established by Zrotowski (see [Z1], [CWZ] and [Z2]) that for non-Mahlo κ, not only is the above condition sufficient but also necessary for P(κ)/ℑ to be $κ^+$-complete. In the present note we are going to visualize that Zrotowski's result is a consequence of the Boolean structure of P(κ) exclusively, rather than of its other particular properties.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Morawiec A.

1 Węglorz B.

1 1993

Wyniki wyszukiwania

Prenormality of ideals and completeness of their quotient algebras