## 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:

 30000 Ordered sets and their cofinalities; pcf theory 3e+35 Consistency and independence results 3e+55 Large cardinals

### Keywords:

cofinality; partially ordered sets
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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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