Borel Tukey morphisms and combinatorial cardinal invariants of the continuum

Samuel Coskey, Tamás Mátrai, and Juris Steprāns. "Borel Tukey morphisms and combinatorial cardinal invariants of the continuum." Fundamenta Mathematicae 223.1 (2013): 29-48. <http://eudml.org/doc/286468>.

@article{SamuelCoskey2013,
abstract = {We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we use our results to give an embedding from the inclusion ordering on 𝒫(ω) into the Borel Tukey ordering on cardinal invariants.},
author = {Samuel Coskey, Tamás Mátrai, Juris Steprāns},
journal = {Fundamenta Mathematicae},
keywords = {cardinal invariants; descriptive set theory; Tukey order; splitting number},
language = {eng},
number = {1},
pages = {29-48},
title = {Borel Tukey morphisms and combinatorial cardinal invariants of the continuum},
url = {http://eudml.org/doc/286468},
volume = {223},
year = {2013},
}

TY - JOUR
AU - Samuel Coskey
AU - Tamás Mátrai
AU - Juris Steprāns
TI - Borel Tukey morphisms and combinatorial cardinal invariants of the continuum
JO - Fundamenta Mathematicae
PY - 2013
VL - 223
IS - 1
SP - 29
EP - 48
AB - We discuss the Borel Tukey ordering on cardinal invariants of the continuum. We observe that this ordering makes sense for a larger class of cardinals than has previously been considered. We then provide a Borel version of a large portion of van Douwen's diagram. For instance, although the usual proof of the inequality 𝔭 ≤ 𝔟 does not provide a Borel Tukey map, we show that in fact there is one. Afterwards, we revisit a result of Mildenberger concerning a generalization of the unsplitting and splitting numbers. Lastly, we use our results to give an embedding from the inclusion ordering on 𝒫(ω) into the Borel Tukey ordering on cardinal invariants.
LA - eng
KW - cardinal invariants; descriptive set theory; Tukey order; splitting number
UR - http://eudml.org/doc/286468
ER -