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On changing cofinality of partially ordered sets. (English) Zbl 1203.03061

Let (\(\ast\)) assert that \((\text{cof} (P))^W = (\text{cof} (P))^V\) whenever \(P\) is a partially ordered set, and \(W\) is an extension of \(V\) with the same ordinals and such that every regular cardinal of \(V\) remains such in \(W\). The author shows that (\(\ast\)) holds if \(2^\kappa < \kappa^{+\omega}\) for every cardinal \(\kappa\), but also that it is consistent relative to \(\omega\) measurable cardinals that \((\ast)\) fails. This answers a question of S. Watson and A. Dow.

MSC:

03E04 Ordered sets and their cofinalities; pcf theory
03E35 Consistency and independence results
03E55 Large cardinals
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References:

[1] Disserlationes Mathematicae 68 (1970)
[2] The core model 61 (1982)
[3] Handbook of set theory
[4] Handbook of set theory
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