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The index set of the groups autostable relative to strong constructivizations
We obtain an exact bound for the algorithmic complexity of the class of strongly constructivizable computable groups that are autostable relative to...
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The Theory of Projective Planes is Complete with Respect to Degree Spectra and Effective Dimensions
We prove that the theory of Pappian projective planes is complete with respect to degree spectra of automorphically nontrivial structures, effective...
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Δ
2 0 -Categoricity of Boolean AlgebrasWe show that the notions of Δ
2 0 -categoricity and relative Δ2 0 -categoricity in Boolean algebras coincide. We prove that for every Turing degree d ... -
Good Structures and Good Theories
In this chapter, we initiate a systematic study of important classes of structures and theories. Of particular importance are saturated structures...
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Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations
We say that a structure is categorical relative to n-decidable presentations ( or autostable relative to n-constructivizations ) if any two n-decidable...
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A Schema for Duality, Illustrated by Bosonization
In this paper we present a schema for describing dualities between physical theories (Sects. 2 and 3), and illustrate it in detail with the example...
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Hyperarithmetical Categoricity of Boolean Algebras of Type \( \mathfrak{B} \)(ω α × η)
We study the Δ
β 0 -categoricity of Boolean algebras. We prove that if δ is a limit ordinal or 0, n ∈ ω, and δ+n ≥ 1, then the Boolean algebra... -
Freely Generated Projective Planes with Finite Computable Dimension
It is proved that for every natural n ≥ 1, there exists a computable freely generated projective plane with computable dimension n . It is stated that...
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Computable dimension for ordered fields
The computable dimension of a structure counts the number of computable copies up to computable isomorphism. In this paper, we consider the possible...
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Reflections on Science and Technology
As soon as he entered MIT Wiener stripped himself of his former image of a professional philosopher and also stopped almost all the channels of...
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Degrees of categoricity for superatomic Boolean algebras
It is proved that every computable superatomic Boolean algebra has a strong degree of categoricity.
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Boolean Algebras with Distinguished Endomorphisms and Generating Trees
We characterize computable Boolean algebras with distinguished endomorphisms in terms of generating trees and map**s of these trees. We show that...
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Ash’s Theorem on Δ
α 0 -Categorical Structures and a Condition for Infinite Δα 0 -DimensionAn old classical result in computable structure theory is Ash’s theorem stating that for every computable ordinal α ≥ 2, under some additional...
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Arithmetical Isomorphisms of Abelian p-Groups
We estimate Turing degrees relative to which the isomorphisms between computable copies of Abelian p-groups possessing complete parts and reduced...
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Computable categoricity of the Boolean algebra \( \mathfrak{B}\left( \omega \right) \) with a distinguished automorphism
It is proved that every computably enumerable Turing degree is a degree of categoricity of some computable Boolean algebra with a distinguished...
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Index Sets of Almost Prime Constructive Models
We study complexity of index sets of strongly constructive almost prime models, almost prime constructive models, and almost prime with strong...