# Blog Archives

# Topic Archive: Harrington's Principle

Set theory seminarMonday, March 30, 20155:00 pmGC 3309

# Harrington’s Principle and remarkable cardinals

University of Münster

It is open whether $\Pi^1_1$ determinacy implies the existence of $0^{\#}$ in 3rd order arithmetic, call it $Z_3$. We compute the large cardinal strength of $Z_3$ plus “there is a real $x$ such that every $x$-admissible is an $L$-cardinal.” This is joint work with Yong Cheng.