<div class="csl-bib-body">
<div class="csl-entry">Andrews, U., Gonzalez, D., Lempp, S., Rossegger, D., & Zhu, H. (2025). The Borel complexity of the class of models of first-order theories. <i>Proceedings of the American Mathematical Society</i>, <i>153</i>(9), 4013–4024. https://doi.org/10.1090/proc/17308</div>
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dc.identifier.issn
0002-9939
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/221309
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dc.description.abstract
We investigate the descriptive complexity of the set of models of first-order theories. Using classical results of Knight and Solovay, we give a sharp condition for complete theories to have a ∏⁰ω-complete set of models. In particular, any sequential theory (a class of foundational theories isolated by Pudlák) has a ∏⁰ω-complete set of models. We also give sharp conditions for theories to have a ∏⁰ₙ-complete set of models.
en
dc.description.sponsorship
European Commission
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dc.description.sponsorship
FWF - Österr. Wissenschaftsfonds
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dc.language.iso
en
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dc.publisher
AMER MATHEMATICAL SOC
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dc.relation.ispartof
Proceedings of the American Mathematical Society
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dc.subject
Borel complexity
en
dc.subject
countable models
en
dc.subject
descriptive set theory
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dc.subject
Models of arithmetic
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dc.title
The Borel complexity of the class of models of first-order theories
