Satisfaction classes with approximate disjunctive correctness

Abstract

We present two new constructions of satisfaction/truth classes over models of PA (Peano Arithmetic) that provide a foil to the fact that the existence of a disjunctively correct full truth class over a model M of PA implies that Con(PA) holds in M.

16 pages. This is a modified version of the paper published in the Review of Symbolic Logic (with the same title). See the note at the beginning of the paper for a description of the modifications. In this version, Definition 2.2.5(g) is fine-tuned