<div class="csl-bib-body">
<div class="csl-entry">Eagle, C. J., Hamel, C., Müller, S., & Tall, F. D. (2023). An undecidable extension of Morley’s theorem on the number of countable models. <i>Annals of Pure and Applied Logic</i>, <i>174</i>(9), Article 103317. https://doi.org/10.1016/j.apal.2023.103317</div>
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dc.identifier.issn
0168-0072
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/191968
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dc.description.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.
en
dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
ELSEVIER
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dc.relation.ispartof
Annals of Pure and Applied Logic
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dc.subject
Countable models
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dc.subject
Inner model theory
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dc.subject
Morley's theorem
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dc.subject
Random and Cohen forcing
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dc.subject
Woodin cardinals
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dc.subject
σ-projective equivalence relations
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dc.title
An undecidable extension of Morley's theorem on the number of countable models