The $\omega$-Vaught's Conjecture

Antonio Montalb\'an; David Gonzalez

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The ω-Vaught's Conjecture

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arxiv 2211.02156 v1 pith:ZLRQ3ICU submitted 2022-11-03 math.LO

The $\omega$-Vaught's Conjecture

David Gonzalez , Antonio Montalb\'an This is my paper

classification math.LO

keywords conjecturevaughtomegainfinitaryproofbelieveconditionequivalent

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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.

The $\omega$-Vaught's Conjecture

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