Possible Worlds, Incompleteness and Undefinability

TL;DR

This paper explores how a broader G"odel numbering approach to possible worlds can create two-world systems that avoid undecidable sentences and the Liar paradox, offering insights into logical consistency.

Contribution

It introduces a novel approach to G"odel numbering that simplifies the handling of possible worlds and bypasses classical logical paradoxes.

Findings

Two-world systems can avoid undecidable sentences

Broader G"odel numbering helps sidestep the Liar paradox

New perspective on possible worlds and logical consistency

Abstract

This short squib looks at how using a broader definition of G\"odel numbering to mimic the accessibility relation between possible worlds results in two-world systems that sidestep undecidable sentences as well as the Liar paradox.