A note on strong negative partition relations

Todd Eisworth. "A note on strong negative partition relations." Fundamenta Mathematicae 202.2 (2009): 97-123. <http://eudml.org/doc/282727>.

@article{ToddEisworth2009,
abstract = {We analyze a natural function definable from a scale at a singular cardinal, and use it to obtain some strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main result makes use of club-guessing, and as a corollary we obtain a fairly easy proof of a difficult result of Shelah connecting weak saturation of a certain club-guessing ideal with strong failures of square-brackets partition relations. We then investigate the strength of weak saturation of such ideals and obtain some results on stationary reflection.},
author = {Todd Eisworth},
journal = {Fundamenta Mathematicae},
keywords = {successors of singular cardinals; scales; square-brackets partition relations; club guessing},
language = {eng},
number = {2},
pages = {97-123},
title = {A note on strong negative partition relations},
url = {http://eudml.org/doc/282727},
volume = {202},
year = {2009},
}

TY - JOUR
AU - Todd Eisworth
TI - A note on strong negative partition relations
JO - Fundamenta Mathematicae
PY - 2009
VL - 202
IS - 2
SP - 97
EP - 123
AB - We analyze a natural function definable from a scale at a singular cardinal, and use it to obtain some strong negative square-brackets partition relations at successors of singular cardinals. The proof of our main result makes use of club-guessing, and as a corollary we obtain a fairly easy proof of a difficult result of Shelah connecting weak saturation of a certain club-guessing ideal with strong failures of square-brackets partition relations. We then investigate the strength of weak saturation of such ideals and obtain some results on stationary reflection.
LA - eng
KW - successors of singular cardinals; scales; square-brackets partition relations; club guessing
UR - http://eudml.org/doc/282727
ER -