There is no classification of the decidably presentable structures

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There Is No Classification of the Decidably Presentable Structures

A computable structure A is decidable if, given a formula φ(x̄) of elementary first-order logic, and a tuple ā ∈ A, we have a decision procedure to decide whether φ holds of ā. We show that there is no reasonable classification of the decidably presentable structures. Formally, we show that the index set of the computable structures with decidable presentations is Σ1-complete. This result holds ...

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ژورنال

عنوان ژورنال: Journal of Mathematical Logic

سال: 2018

ISSN: 0219-0613,1793-6691

DOI: 10.1142/s0219061318500101