| Friday 10 January 2025 | |
| Events for day: Thursday 09 January 2025 |
| 14:00 - 16:00 Mathematical Logic Weekly Seminar Can You Take Komjath's Inaccessible Away? School MATHEMATICS We aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the effect of large cardinal assumptions on this comparison. Using the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains an Aronszajn subtree, if there is an inaccessible cardinal. This is stronger than a therm due to Komjath where he proves the same consistency from two inaccessible cardinals. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree T such that if U ⊂ T is a Kurepa tree with the inherited order from T, then U has an Aronszajn subtree. This theorem uses no ... |