Coherent ultrafilters and nonhomogeneity

Starý, Jan. "Coherent ultrafilters and nonhomogeneity." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 257-264. <http://eudml.org/doc/270093>.

@article{Starý2015,
abstract = {We introduce the notion of a coherent $P$-ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a $P$-point on $\omega $, and show that these ultrafilters exist generically under $\mathfrak \{c\} = \mathfrak \{d\}$. This improves the known existence result of Ketonen [On the existence of $P$-points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1, 233–241] can be extended to show that coherently selective ultrafilters exist generically under $\mathfrak \{c\} = \operatorname\{cov\}\mathcal \{M\}$. We use these ultrafilters in a topological application: a coherent $P$-ultrafilter on an algebra $\mathcal \{B\}$ is an untouchable point in the Stone space of $\mathcal \{B\}$, witnessing its nonhomogeneity.},
author = {Starý, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nonhomogeneity; ultrafilter; Boolean algebra; untouchable point},
language = {eng},
number = {2},
pages = {257-264},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Coherent ultrafilters and nonhomogeneity},
url = {http://eudml.org/doc/270093},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Starý, Jan
TI - Coherent ultrafilters and nonhomogeneity
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 257
EP - 264
AB - We introduce the notion of a coherent $P$-ultrafilter on a complete ccc Boolean algebra, strengthening the notion of a $P$-point on $\omega $, and show that these ultrafilters exist generically under $\mathfrak {c} = \mathfrak {d}$. This improves the known existence result of Ketonen [On the existence of $P$-points in the Stone-Čech compactification of integers, Fund. Math. 92 (1976), 91–94]. Similarly, the existence theorem of Canjar [On the generic existence of special ultrafilters, Proc. Amer. Math. Soc. 110 (1990), no. 1, 233–241] can be extended to show that coherently selective ultrafilters exist generically under $\mathfrak {c} = \operatorname{cov}\mathcal {M}$. We use these ultrafilters in a topological application: a coherent $P$-ultrafilter on an algebra $\mathcal {B}$ is an untouchable point in the Stone space of $\mathcal {B}$, witnessing its nonhomogeneity.
LA - eng
KW - nonhomogeneity; ultrafilter; Boolean algebra; untouchable point
UR - http://eudml.org/doc/270093
ER -