Some Remarks on Generalized Martin's Axiom
Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 135
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
Let $GMA$ denote that if ${\Bbb P}$ is well-met, strongly
$\omega_1$-closed and $\omega_1$-centered partial order and ${\Cal D}$
a family of $2^{\omega_1}$ dense subsets of ${\Bbb P}$: then there is
a filter $G\subseteq {\Bbb P}$ which meets every member of ${\Cal D}$.
The consistency of $2^\omega = \omega_1 + 2^{\omega_1}>\omega_2 + GMA$
was proved by Baumgartner [1] and in [13] many of its consequences were
considered. In this paper we give a consequence and present an
independence result. Namely, we prove that, as a consequence of
$2^\omega = \omega_1 + 2^{\omega_1}>\omega_2 + GMA$, every
$\leq^*$-increasing $\omega_2$-sequence in
$(\omega_1^{\omega_1},\leq^*)$ is a lower half of some
$(\omega_2,\omega_2)$-gap and show that the existence of an
$\omega_2$-Kurepa tree is consistent with and independent of
$2^\omega = \omega_1 + 2^{\omega_1}>\omega_2 + GMA$.
Classification :
03E35
@article{PIM_1995_N_S_57_71_a13,
author = {Z. Spasojevi\'c},
title = {Some {Remarks} on {Generalized} {Martin's} {Axiom}},
journal = {Publications de l'Institut Math\'ematique},
pages = {135 },
publisher = {mathdoc},
volume = {_N_S_57},
number = {71},
year = {1995},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a13/}
}
Z. Spasojević. Some Remarks on Generalized Martin's Axiom. Publications de l'Institut Mathématique, _N_S_57 (1995) no. 71, p. 135 . http://geodesic.mathdoc.fr/item/PIM_1995_N_S_57_71_a13/