Published online by Cambridge University Press: 12 March 2014
We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing and we obtain a cardinal invariant such that collapses the continuum to and . Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of . We define two relations and on the set (ωω)Fin of finite-to-one functions which are Tukey equivalent to the eventual dominance relation of functions such that if -unbounded, well-ordered by , and not -dominating, then there is a nonmeager p-ideal. The existence of such a system follows from Martin's axiom. This is an analogue of the results of [3], [9, 10] for increasing functions.
To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.
To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.