The $\omega$-Vaught's Conjecture

David Gonzalez; Antonio Montalbán

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arXiv · 2211.02156

The $\omega$-Vaught's Conjecture

David Gonzalez·Antonio Montalbán

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Abstract

We introduce the $\omega$-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 $\omega$-Vaught's conjecture. We show the existence of an equivalent condition to the $\omega$-Vaught's conjecture and use this tool to show that all infinitary sentences whose models are linear orders satisfy the $\omega$-Vaught's conjecture.

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BibTeX RIS

David Gonzalez, Antonio Montalbán. 2022-11-03. The $\omega$-Vaught's Conjecture. https://arxiv.org/abs/2211.02156

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