Geodesic
Recursive expansions
Fundamenta Mathematicae, Tome 145 (1994) no. 2, pp. 153-169 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let A be a recursive structure, and let ψ be a recursive infinitary ${Π}_2$ sentence involving a new relation symbol. The main result of the paper gives syntactical conditions which are necessary and sufficient for every recursive copy of A to have a recursive expansion to a model of ψ, provided A satisfies certain decidability conditions. The decidability conditions involve a notion of rank. The main result is applied to prove some earlier results of Metakides-Nerode and Goncharov. In these applications, the ranks turn out to be low, but there are examples in which the rank takes arbitrary recursive ordinal values.
DOI : 10.4064/fm-145-2-153-169

C. Ash 1 ; J. Knight 1

1 
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C. Ash; J. Knight. Recursive expansions. Fundamenta Mathematicae, Tome 145 (1994) no. 2, pp. 153-169. doi: 10.4064/fm-145-2-153-169

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