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Grantor: Austrian Science Foundation (FWF) - Czech Science Foudation

**Objectives**:

The project falls within the scope of Set Theory & Foundations of Mathematics, specifically Combinatorial Set Theory and Forcing. We will investigate new combinatorial and forcing methods for constructing ultrafilters with special properties in different models of Set Theory.It will use these methods to answer independence questions about ultrafilters (no P-points with a large continuum or small character filters), structural questions about filters (which ultrafilters/filters contain towers) and questions about the related cardinal invariants (independence number, free sequence number). It is known that current methods cannot answer some of these questions so the project will have to come up with novel ideas. The methods used will include forcing iterations, diamond-like constructions, preservation theorems and methods from descriptive set theory.

IM leader :

Main investigator:

**Verner** Jonathan

IM team members:

Grebík Jan |

Participating institutions:

Faculty of Arts, Charles University in Prague,** Coordinator**

Institute of Mathematics, Czech Academy of Sciences

TU Wien