Eagle, C. J., Hamel, C., Müller, S., & Tall, F. D. (2023). An undecidable extension of Morley’s theorem on the number of countable models. Annals of Pure and Applied Logic, 174(9), Article 103317. https://doi.org/10.1016/j.apal.2023.103317
Countable models; Inner model theory; Morley's theorem; Random and Cohen forcing; Woodin cardinals; σ-projective equivalence relations
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Abstract:
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory.
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Project title:
Lange Spiele und Determiniertheit wenn alle Mengen uB sind: V 844-N (FWF - Österr. Wissenschaftsfonds) Determiniertheit und Woodin Limes von Woodin Kardinalzahlen: Y1498 (FWF - Österr. Wissenschaftsfonds) Klassifikation abgeleiteter Modelle der Determiniertheit: I6087-N (FWF - Österr. Wissenschaftsfonds)
