6 papers · 1 filter
Ranking theories via encoded -models
Hanul Jeon, Patrick Lutz, Fedor Pakhomov +1
Ranking theories according to their strength is a recurring motif in mathematical logic. We introduce a new ranking of arbitrary (not necessarily recursively axiomatized) theories…
Martin's measurable dilator
Hanul Jeon
Martin's remarkable proof of -determinacy from an iterable rank-into-rank embedding highlighted the connection between large cardinals and determinacy. In this paper,…
Proof-theoretic dilator and intermediate pointclasses
Hanul Jeon
There are two major generalizations of the standard ordinal analysis: One is Girard's -proof theory in which dilators are assigned to theories instead of ordinals. The other…
On a cofinal Reinhardt embedding without Powerset
Hanul Jeon
In this paper, we provide a positive answer to the question of Matthews whether is consistent with a non-trivial cofinal Reinhardt elementary embedding $j\colon V\t…
The behavior of higher proof theory I: Case
Hanul Jeon
Walsh [MR4525964, Zbl 1569.03151] has shown that comparing proof-theoretic ordinals is equivalent to comparing -consequence comparison and -reflection comparison, all…
Generalized ordinal analysis and reflection principles in set theory
Hanul Jeon, James Walsh
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is…