Satisfaction classes with approximate disjunctive correctness

TL;DR

This paper introduces two novel constructions of satisfaction classes in models of Peano Arithmetic, challenging the assumption that disjunctive correctness implies consistency of PA within the model.

Contribution

It provides new methods for constructing satisfaction classes that serve as counterexamples to previous beliefs about disjunctive correctness and consistency.

Findings

Constructed two satisfaction classes with approximate disjunctive correctness.

Showed that disjunctively correct truth classes do not necessarily imply Con(PA).

Challenged existing assumptions about truth classes in models of PA.

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.