Local classes and computable indexations
The author investigates some properties of constructive models in the sense of \textit{Yu. L. Ershov} [Decision problems and constructivizable models (Russian) (1980; Zbl 0495.03009)]. A notion of reducibility \(\leq_{\ell.c.}\), compatible with local classes, is introduced. The author shows that if a class \(K^*\) of constructive models has two computable indexings \(\alpha\) and \(\gamma\) such that \(\alpha\leq_{\ell.c.}\gamma\) then there exists a computable indexing \(\tau\) of the same class so that \(\alpha\) \(\nleq_{\ell.c.}\tau\), \(\gamma\) \(<_{\ell.c.}\tau\) and \(\tau\leq_{\ell.c.}\gamma.\) A sufficient condition under which a computable class K of constructive models has infinitely many incomparable indexings, is obtained. A number of other results are dispersed throughout the paper.
scientific article; zbMATH DE number 4087653