Splitting families of sets
Seminar
Speaker
Tal Kagalovsky (BGU)
Date
02/05/2024 - 16:00 - 14:00Add to Calendar
2024-05-02 14:00:00
2024-05-02 16:00:00
Splitting families of sets
I will present several known results in the topic of splitting families of sets. Miller’s splitting theorem from 1937 was proven for finite n > 0 and ρ-uniform families where ρ is infinite. Under the assumptions of GCH and without the use of more modern tools, this approach is generalized here in order to prove several stronger theorems by Erdős and Hajnal.
Then a more modern approach by Kojman will be presented, where he used Shelah’s RGCH in order to eliminate the GCH from some of the theorems when ρ ≥ בω (ν). This was done using filtrations with respect to anti-monotone functions.
Seminar room
אוניברסיטת בר-אילן - המחלקה למתמטיקה
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Seminar room
Abstract
I will present several known results in the topic of splitting families of sets. Miller’s splitting theorem from 1937 was proven for finite n > 0 and ρ-uniform families where ρ is infinite. Under the assumptions of GCH and without the use of more modern tools, this approach is generalized here in order to prove several stronger theorems by Erdős and Hajnal.
Then a more modern approach by Kojman will be presented, where he used Shelah’s RGCH in order to eliminate the GCH from some of the theorems when ρ ≥ בω (ν). This was done using filtrations with respect to anti-monotone functions.
תאריך עדכון אחרון : 15/04/2024
