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 large cardinal assumption. Our last theorem immediately implies the following: If MAω2 holds and ω2 is not a Mahlo cardinal in L then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's ρ function which might be useful in other contexts. This is a joint work with Stevo Todorcevic.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618