THE FILTER DICHOTOMY AND MEDIAL LIMITS

The Filter Dichotomy and medial limits

The Filter Dichotomy says that every uniform nonmeager filter on the integers is mapped by a finite-to-one function to an ultrafilter. The consistency of this principle was proved by Blass and Laflamme. A medial limit is a universally measurable function from P(ω) to the unit interval [0, 1] which is finitely additive for disjoint sets, and maps singletons to 0 and ω to 1. Christensen and Mokob...

The Filter Dichotomy Principle Does Not Imply the Semifilter Trichotomy Principle

We answer Blass' question from 1989 of whether the inequality u < g is strictly stronger than the lter dichotomy principle [6, page 36] a rmatively. We show that there is a forcing extension in which every non-meagre lter on ω is ultra by nite-to-one and the semilter trichotomy does not hold. This trichotomy says: every semi lter is either meagre or comeagre or ultra by nite-to-one. The trichot...

Generalized Covering Groups and Direct Limits

The near Coherence of Filters Principle Does Not Imply the Filter Dichotomy Principle

We show that there is a forcing extension in which any two ultrafilters on ω are nearly coherent and there is a non-meagre filter that is not nearly ultra. This answers Blass’ longstanding question (1989) of whether the principle of near coherence of filters is strictly weaker than the filter dichotomy

The Particle Filter and Extended Kalman Filter methods for the structural system identification considering various uncertainties

Structural system identification using recursive methods has been a research direction of increasing interest in recent decades. The two prominent methods, including the Extended Kalman Filter (EKF) and the Particle Filter (PF), also known as the Sequential Monte Carlo (SMC), are advantageous in this field. In this study, the system identification of a shake table test of a 4-story steel struct...