ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: 03D55, 03D70 Hartz, David, College of St. Benedict Hierarchy Based on Inductive Definitions Let Q be an inductive operator on ω. The stages of the inductive definition determined by Q are Q_{σ}(x) ↔ (∃τ < σ)Q(Q_{τ} , x). We define a hierarchy of sets of natural numbers as follows: A relation P is I_{ρσ} if P is many-one reducible to Q_{σ} where Q is Σ_{ρ}^{0}, and P is J_{ρσ} for a successor ordinal σ if P is many-one reducible to Q_{σ} where Q is Π_{ρ}^{0}. This hierarchy is an extension of the hyperarithmetic hierarchy that extends at least as far as the closure ordinal for Δ_{1}^{1} inductive definitions, and it has an additional advantage of not being dependent on ordinal notations.