Rowbottom-type properties and a cardinal arithmetic
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- by Jan Tryba PDF
- Proc. Amer. Math. Soc. 96 (1986), 661-667 Request permission
Abstract:
Assuming Rowbottom-type properties, we estimate the size of certain families of closed disjoint functions. We show that whenever $k$ is Rowbottom and ${2^\omega } < {\aleph _{{\omega _1}}}(k)$, then ${2^{ < k}} = {2^\omega }$ or $k$ is the strong limit cardinal. Next we notice that every strongly inaccessible Jónsson cardinal $k$ is $v$-Rowbottom for some $v < k$. In turn, Shelah’s method allows us to construct a Jónsson model of cardinality ${k^ + }$ provided ${k^{{\text {cf(}}k{\text {)}}}} = {k^ + }$. We include some additional remarks.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 96 (1986), 661-667
- MSC: Primary 03E10; Secondary 03C50, 03E05, 03E55
- DOI: https://doi.org/10.1090/S0002-9939-1986-0826499-7
- MathSciNet review: 826499