The Reverse Mathematics of Harrington's Principle

Robert Lubarsky (FAU, Boca Ratón)

Jul 01. 2025, 11:30 — 12:15

Harrington's Principle states that there is a real whose only admissible ordinals are all cardinals in $L$. It has long been known to be equivalent with the existence of $0^\sharp$. That equivalence though is over the base theory ZFC, or, if examined more carefully, fourth-order arithmetic $Z_4$. It was shown by Cheng and Schindler that over $Z_3$ HP does not imply $0^\sharp$, and that $Z_2$ + HP is equiconsistent with ZFC. The goal of this talk is to explain that last result, as well as its refinement to the common subsystems of $Z_2$, namely the equiconsistency of $\Pi^1_n$-Comprehension + HP with the appropriate fragment of ZFC. This is joint work with Juan Aguilera.

Further Information
Venue:
ESI Schrödinger and Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Reverse Mathematics (Thematic Programme)
Organizer(s):
Juan Aguilera (TU Vienna)
Linda Brown Westrick (Penn State U)
Noam Greenberg (Victoria U of Wellington)
Denis Hirschfeldt (U of Chicago)