Splitting families and the Noetherian type of $βω-ω$

Details Splitting families and the Noetherian type of $βω-ω$ Splitting families and the Noetherian type of $βω-ω$

2007-05-29

arxiv.org/abs/0705.4297v2

Journal of Symbolic Logic 73 (2008), no. 4, 1289--1306

Mathematics

Logic

This version accepted for publication by Journal of Symbolic Logic. Fixed typos. Removed Lemma 5.10 due to bug in its proof

Scientific paper

Extending some results of Malykhin, we prove several independence results about base properties of $\beta\omega-\omega$ and its powers, especially the Noetherian type $Nt(\beta\omega-\omega)$, the least $\kappa$ for which $\beta\omega-\omega$ has a base that is $\kappa$-like with respect to containment. For example, $Nt(\beta\omega-\omega)$ is never less than the splitting number, but can consistently be that $\omega_1$, $2^\omega$, $(2^\omega)^+$, or strictly between $\omega_1$ and $2^\omega$. $Nt(\beta\omega-\omega)$ is also consistently less than the additivity of the meager ideal. $Nt(\beta\omega-\omega)$ is closely related to the existence of special kinds of splitting families.

Affiliated with

Also associated with

No associations

Rating

Splitting families and the Noetherian type of $βω-ω$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Splitting families and the Noetherian type of $βω-ω$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Splitting families and the Noetherian type of $βω-ω$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-356696