autostability of prime models under strong constructivizations

Гончаров, С. С.

doi:10.1007/s10469-009-9072-y

Cited by 10 publications

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References 23 publications

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“…On the other hand, the index set of relatively computably categorical structures is Σ 0 3 -complete [2]. More recently, Goncharov started to study the complexity of the notion of categoricity restricted to decidable structures [9][10][11].…”

Section: Definitionmentioning

confidence: 99%

Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations

et al. 2015

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Keywords: index set, structure categorical relative to n-decidable presentations, n-decidable structure 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 copies of the structure are computably isomorphic. For n = 0, we have the classical definition of a computably categorical (autostable) structure. Downey, Kach, Lempp, Lewis, Montalbán, and Turetsky proved that there is no simple syntactic characterization of computable categoricity. More formally, they showed that the index set of computably categorical structures is Π 1 1 -complete. Here we study index sets of n-decidable structures that are categorical relative to m-decidable presentations, for various m, n ∈ ω. If m ≥ n ≥ 0, then the index set is again Π 1 1 -complete, i.e., there is no nice description of the class of n-decidable structures that are categorical relative to m-decidable presentations. In the case m = n − 1 ≥ 0, the index set is Π 0 4 -complete, while if 0 ≤ m ≤ n − 2, the index set is Σ 0 3 -complete. * Supported by Austrian Science Fund FWF (projects V 206 and I 1238).

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Section: Definitionmentioning

confidence: 99%

Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations

et al. 2015

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“…В этом разделе мы изучим вопрос о наследовании автоустойчивости относительно сильных конструктивизаций в простых относительно обогащения константами моделях. Будем следовать работе [35].…”

Section: эренфойхтова теория с автоустойчивой простой модельюunclassified

Об Автоустойчивости Относительно Сильных Конструктивизаций Почти Простых Моделей

Гончаров¹,

Goncharov²

2010

Uspekhi Mat. Nauk

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The Degree of Decidable Categoricity of a Model with Infinite Solutions for Complete Formulas

Goncharov

Marchuk

2021

Algebra Logic

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autostability of prime models under strong constructivizations

Abstract: We furnish an example of an Ehrenfeucht theory whose prime model is autostable under strong constructivizations and there exists a prime model in a finite expansion by constants that is nonautostable under strong constructivizations of the theory constructed.

Cited by 10 publications

References 23 publications

Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations

Index Sets for n-Decidable Structures Categorical Relative to m-Decidable Presentations

Об Автоустойчивости Относительно Сильных Конструктивизаций Почти Простых Моделей

The Degree of Decidable Categoricity of a Model with Infinite Solutions for Complete Formulas

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