# Mgr. Jonathan Verner, PhD.

I am a researcher at the Department of Logic. My research focuses on Set Theory. In particular I am excited by filters and ultrafilters, forcing, infinite combinatorics and the structure of the real line. Occasionally I also dabble into large cardinals (again mostly either in connection with ultrafilters or forcing or both).

## Publications

### Articles (12)

#### 2018

, Chains of P-points (submitted)
, Completely separably MAD families and the modal logic of $\beta\omega$ (preprint)
, Ramsey partitions of metric spaces (preprint)
, , Towers in Filters, Cardinal Invariants and Luzin Type Families Journal of Symbolic Logic, 2018

#### 2016

, A lifting argument for generalized Gregorieff forcing Notre Dame Journal of Formal Logic, 2016 57 (2) 57 (2) 2016 221-231
, $G_\delta$ and co-meager semifilters Fundamenta Mathematicae, 2016 235 2016 153-166

#### 2013

Filter convergence in $\beta\omega$ Acta Universitatis Carolinae. Philosophica et Historica, 2010 2 2 2013 87-90
Lonely points revisited Commentationes Mathematicae Universitatis Carolinae, 54 1 1 2013 105-110
, , On strong $P$-points
On strong P-points 2013 2875-2883

#### 2011

, Adding ultrafilters by definable quotients Rendiconti del Circolo Matematico di Palermo, 60 3 3 2011 445-454

#### 2008

Lonely points in ω*

### Other (2)

#### 2016

, Toposym Book of Abstracts 2016

#### 2011

, Toposym 2011 Book of Abstracts 2011