Chang's Conjecture, club-increasing sequences, and P_max forcing, part 1

Seminar
Speaker
Chris Lambie-Hanson (BIU)
Date
28/05/2018 - 15:00 - 13:00Add to Calendar 2018-05-28 13:00:00 2018-05-28 15:00:00 Chang's Conjecture, club-increasing sequences, and P_max forcing, part 1 The consistency of the Chang's Conjecture (CC) variant (aleph_{omega + 1}, aleph_omega) ->> (aleph_2, aleph_1) is a major open question. A combinatorial consequence of this instance of CC is the existence of a certain strongly increasing sequence, of length aleph_2, of functions from omega to some fixed ordinal below omega_2 (we are calling such a sequence a club-increasing sequence). In response to a question from the speaker, Paul Larson proved the consistency of the existence of a club-increasing sequence of length aleph_2 using a P_max forcing variation. In this talk, we will prove some basic results about club-increasing sequences, including the facts that their existence follows from the relevant instance of CC and that club-increasing sequences of length omega_n do not exist for n at least 4. We will then give an introduction to P_max forcing, in preparation for a future talk in which we will present a sketch of Larson's proof. Building 507, Room 204 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 507, Room 204
Abstract

The consistency of the Chang's Conjecture (CC) variant (aleph_{omega + 1}, aleph_omega) ->> (aleph_2, aleph_1) is a major open question. A combinatorial consequence of this instance of CC is the existence of a certain strongly increasing sequence, of length aleph_2, of functions from omega to some fixed ordinal below omega_2 (we are calling such a sequence a club-increasing sequence). In response to a question from the speaker, Paul Larson proved the consistency of the existence of a club-increasing sequence of length aleph_2 using a P_max forcing variation. In this talk, we will prove some basic results about club-increasing sequences, including the facts that their existence follows from the relevant instance of CC and that club-increasing sequences of length omega_n do not exist for n at least 4. We will then give an introduction to P_max forcing, in preparation for a future talk in which we will present a sketch of Larson's proof.

תאריך עדכון אחרון : 28/10/2019