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APPLICATIONS OF PCF THEORY TO THE STUDY OF IDEALS ON ![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220908201216861-0586:S0022481222000044:S0022481222000044_inline1.png?pub-status=live)
Published online by Cambridge University Press: 11 January 2022
Abstract
Let
$\kappa $
be a regular uncountable cardinal, and
a cardinal greater than or equal to
$\kappa $
. Revisiting a celebrated result of Shelah, we show that if
is close to
$\kappa $
and
(= the least size of a cofinal subset of
) is greater than
, then
can be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that if
and
, then no
$\kappa $
-complete ideal on
is weakly
-saturated.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic
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