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Topic Archive: Harrington's Principle

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

Ralf Schindler

Harrington’s Principle and remarkable cardinals

University of M√ľnster

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.