The ultrafilter number and $\mathfrak {hm}
The cardinal invariant $\mathfrak {hm}$ is defined as the minimum size of a family of $\mathsf {c}_{\mathsf {min}}$ -monochromatic sets that cover $2^{\omega }$ (where $\mathsf {c}_{\mathsf {min}}( x,y) $ is the parity of the biggest initial segment both x and y have in common). We prove that $\math...
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Veröffentlicht in: | Canadian journal of mathematics 2023-04, Vol.75 (2), p.494-530 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The cardinal invariant
$\mathfrak {hm}$
is defined as the minimum size of a family of
$\mathsf {c}_{\mathsf {min}}$
-monochromatic sets that cover
$2^{\omega }$
(where
$\mathsf {c}_{\mathsf {min}}( x,y) $
is the parity of the biggest initial segment both x and y have in common). We prove that
$\mathfrak {hm}=\omega _{1}$
holds in Shelah’s model of
$\mathfrak {i |
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ISSN: | 0008-414X 1496-4279 |
DOI: | 10.4153/S0008414X21000614 |