# A tree $\pi $-base for ${\mathbb{R}}^{*}$ without cofinal branches

Commentationes Mathematicae Universitatis Carolinae (2005)

- Volume: 46, Issue: 4, page 721-734
- ISSN: 0010-2628

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topHernández-Hernández, Fernando. "A tree $\pi $-base for $\mathbb {R}^\ast $ without cofinal branches." Commentationes Mathematicae Universitatis Carolinae 46.4 (2005): 721-734. <http://eudml.org/doc/249519>.

@article{Hernández2005,

abstract = {We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree $\pi $-base for $\mathbb \{N\}^\{\ast \}$ with no $\omega _\{2\}$ branches yet of height $\omega _\{2\}$. We establish that this is also possible for $\mathbb \{R\}^\{\ast \}$ using a natural modification of Mathias forcing.},

author = {Hernández-Hernández, Fernando},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {distributivity of Boolean algebras; cardinal invariants of the continuum; Stone-Čech compactification; tree $\pi $-base; distributivity of Boolean algebras; cardinal invariants of the continuum; Stone-Čech compactification; tree -base},

language = {eng},

number = {4},

pages = {721-734},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A tree $\pi $-base for $\mathbb \{R\}^\ast $ without cofinal branches},

url = {http://eudml.org/doc/249519},

volume = {46},

year = {2005},

}

TY - JOUR

AU - Hernández-Hernández, Fernando

TI - A tree $\pi $-base for $\mathbb {R}^\ast $ without cofinal branches

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2005

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 46

IS - 4

SP - 721

EP - 734

AB - We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree $\pi $-base for $\mathbb {N}^{\ast }$ with no $\omega _{2}$ branches yet of height $\omega _{2}$. We establish that this is also possible for $\mathbb {R}^{\ast }$ using a natural modification of Mathias forcing.

LA - eng

KW - distributivity of Boolean algebras; cardinal invariants of the continuum; Stone-Čech compactification; tree $\pi $-base; distributivity of Boolean algebras; cardinal invariants of the continuum; Stone-Čech compactification; tree -base

UR - http://eudml.org/doc/249519

ER -

## References

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