DOI

We explore numbered Boolean algebras over levels Ξ of arithmetical and analytical hierarchies. We show the existence and uniqueness (up to computable isomorphism) of universal Boolean Ξ-algebras, determine the levels in which such algebras exist, and classify the universal algebras up to isomorphism. We apply these results to the semantic class of all countable saturated models having decidable ω-stable theories in a fixed finite rich signature. It turns out that the Tarski-Lindenbaum algebra of this class equipped with a Gödel numbering of the sentences is a Boolean Σ11-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean Σ11-algebras. This determines uniquely the isomorphism type of this Boolean algebra.
Язык оригиналаанглийский
Название основной публикацииTwenty Years of Theoretical and Practical Synergies (CiE 2024)
РедакторыLevy Patey
ИздательSpringer Nature
Страницы205–217
Число страниц13
ISBN (печатное издание)9783031643088
DOI
СостояниеОпубликовано - 2024
СобытиеTwenty Years of Theoretical and Practical Synergies: 20th Conference on Computability in Europe - Amsterdam University College, Amsterdam, Нидерланды
Продолжительность: 8 июл 202412 июл 2024
https://events.illc.uva.nl/CiE/CiE2024/Main/

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том14773 LNCS

конференция

конференцияTwenty Years of Theoretical and Practical Synergies
Сокращенное названиеCiE 2024
Страна/TерриторияНидерланды
ГородAmsterdam
Период8/07/2412/07/24
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