Book ChapterDOI
Prime Model with No Degree of Autostability Relative to Strong Constructivizations
Nikolay Bazhenov
- pp 117-126
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A decidable structure is built such that \(\mathcal {M}\) is a prime model of the theory \(Th\) and has no degree of autostability relative to strong constructivizations.Abstract:
We build a decidable structure \(\mathcal {M}\) such that \(\mathcal {M}\) is a prime model of the theory \(Th(\mathcal {M})\) and \(\mathcal {M}\) has no degree of autostability relative to strong constructivizations.read more
Citations
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Journal ArticleDOI
Autostability spectra for decidable structures
TL;DR: It is shown that for an infinite computable ordinal β, every Turing degree c.e. in and above 0 (2β+1) is the degree of SC-autostability for some discrete linear order, and it is proved that the set of all PA-degrees is an SC- autostability spectrum.
Journal ArticleDOI
Categoricity Spectra of Computable Structures
TL;DR: This paper focuses on the results about degrees of categoricity for linear orders and Boolean algebras, and constructs a new series of examples of Degrees of categricity forlinear orders.
Journal ArticleDOI
On Decidable Categoricity and Almost PrimeModels
TL;DR: The degree of categoricity of various prime models with added constants, also called almost prime models, is investigated, and the Turing degree of the set C(\mathcal {M}) of complete formulas is related to the Turing level of that set.
References
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Book
Computable structures and the hyperarithmetical hierarchy
TL;DR: Theorems of Barker and Davey and the Barwise-Kreisel Compactness Theorem lead to the existence of computable structures.
Journal ArticleDOI
Effective Procedures in Field Theory
A. Fröhlich,John C. Shepherdson +1 more
TL;DR: This paper sharpen van der Waerden’s result on the non-existence of a general splitting algorithm by constructing a particular explicitly given field which has no splitting algorithm and shows that the results on the existence of a splitting algorithm for a finite extension field does not hold for inseparable extensions.
Journal ArticleDOI
Constructive algebras i
TL;DR: In this article, the authors introduce algebraic systems and define relations between functions, operations, predicates, and sets, and present finitely generated algebras of recursive functions and homomorphisms and congruences.