A dichotomy for transitive lists, part 1
Seminar
Speaker
Roy Shalev (BIU)
Date
13/02/2025 - 17:00 - 15:00Add to Calendar
2025-02-13 15:00:00
2025-02-13 17:00:00
A dichotomy for transitive lists, part 1
We present a dichotomy statement concerning a subclass of transitive lists which is a consequence of Martin's Axiom and in fact follows both from K'_2 and from the Martin Axiom for Y-cc posets.
This dichotomy implies that the bounding number is bigger than w1, that every w1-Aronszajn tree is special, moreover, that there are no w1-Souslin lower semi-lattices.
Next, we prove that an higher analog for w2 of the dichotomy is consistent with CH, assuming the existence of a weakly compact cardinal.
This result extends the Laver-Shelah theorem on the consistency of CH with the w2-Souslin Hypothesis, as here one gets a CH model with no w2-Souslin lower semi-lattices.
Based on a joint work with Stevo Todorčević and Boriša Kuzeljević.
Seminar room
אוניברסיטת בר-אילן - Department of Mathematics
mathoffice@math.biu.ac.il
Asia/Jerusalem
public
Place
Seminar room
Abstract
We present a dichotomy statement concerning a subclass of transitive lists which is a consequence of Martin's Axiom and in fact follows both from K'_2 and from the Martin Axiom for Y-cc posets.
This dichotomy implies that the bounding number is bigger than w1, that every w1-Aronszajn tree is special, moreover, that there are no w1-Souslin lower semi-lattices.
Next, we prove that an higher analog for w2 of the dichotomy is consistent with CH, assuming the existence of a weakly compact cardinal.
This result extends the Laver-Shelah theorem on the consistency of CH with the w2-Souslin Hypothesis, as here one gets a CH model with no w2-Souslin lower semi-lattices.
Based on a joint work with Stevo Todorčević and Boriša Kuzeljević.
Last Updated Date : 09/02/2025
