Geodesic
Relatively recursive expansions
Fundamenta Mathematicae, Tome 140 (1991) no. 2, pp. 137-155

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

In this paper, we consider the following basic question. Let A be an L-structure and let ψ be an infinitary sentence in the language L∪{R}, where R is a new relation symbol. When is it the case that for every B ≅ A, there is a relation R such that (B,R) ⊨ ψ and $R ≤_T D(B)$? We succeed in giving necessary and sufficient conditions in the case where ψ is a "recursive" infinitary $Π_2$ sentence. (A recursive infinitary formula is an infinitary formula with recursive disjunctions and conjunctions.) We consider also some variants of the basic question, in which R is r.e., $Δ_α^0$, or $Σ_α$ instead of recursive relative to D(B).
DOI : 10.4064/fm-140-2-137-155

C. Ash 1 ; J. Knight 1

1 
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C. Ash; J. Knight. Relatively recursive expansions. Fundamenta Mathematicae, Tome 140 (1991) no. 2, pp. 137-155. doi: 10.4064/fm-140-2-137-155

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