The $\omega$-Vaught's Conjecture
Logic
2022-11-07 v1
Abstract
We introduce the -Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion theory, then the proof would probably be a proof of the -Vaught's conjecture. We show the existence of an equivalent condition to the -Vaught's conjecture and use this tool to show that all infinitary sentences whose models are linear orders satisfy the -Vaught's conjecture.
Cite
@article{arxiv.2211.02156,
title = {The $\omega$-Vaught's Conjecture},
author = {David Gonzalez and Antonio Montalbán},
journal= {arXiv preprint arXiv:2211.02156},
year = {2022}
}