Type: Article

Construction with opposition: cardinal invariants and games

Brendle, Jörg; Hrusak, Michael; Torres-Pérez, Víctor;

Abstract:

We consider several game versions of the cardinal invariants t , u and a . We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that t < t Builder and u < u Builder are both relatively consistent with ZFC, where t Builder and u Builder are the principal game versions of t and u , respectively. The corresponding question for a remains open. [ABSTRACT FROM AUTHOR] Copyright of Archive for Mathematical Logic is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.