PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 57(71) (dedicated to Djuro Kurepa), pp. 135142 (1995) 

Some remarks on generalized Martin's axiomZ. Spasojevi\'cInstitute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, IsraelAbstract: Let $GMA$ denote that if ${\Bbb P}$ is wellmet, 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 (MSC2000): 03E35 Full text of the article:
Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
