On LP-models of arithmetic

Abstract

We answer some problems set by Priest in [11] and [12], in particular refuting Priest’s Conjecture that all LP-models of Th(ℕ) essentially arise via congruence relations on classical models of Th(ℕ). We also show that the analogue of Priest’s Conjecture for IΔ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂_e M ⊨ IΔ₀ + Exp in any cut [0,a] ⊂_e K ⊆_e M closed under successor and multiplication.