Proof-theoretic dilator and intermediate pointclasses

2025/01/20 by Jeon, Hanul
#03D60 #03F07 #03F15 #03F35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2501.11220

Abstract

There are two major generalizations of the standard ordinal analysis: One is Girard's Π¹₂-proof theory in which dilators are assigned to theories instead of ordinals. The other is Pohlers' generalized ordinal analysis with Spector classes, where ordinals greater than ω₁^CK are assigned to theories. In this paper, we show that these two are systematically entangled, and Σ¹₂-proof theoretic analysis has a critical role in connecting these two.

Related

• The behavior of higher proof theory I: Case Σ¹₂
• A characterization of ordinal analysis
• Characterizations of ordinal analysis
• The Π¹₂ Consequences of a Theory
• Introducing the hardline in proof theory