Splitting Localization and prediction numbers

25.03.2021 15:00 - 16:30

Iván Ongay-Valverde (York University, Canada)

In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are 'tame' somehow (for example, you do not add Cohen or Random reals).

In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.

Impressively, these two notions are related.

In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.



online via Zoom