Recursion Theory I

Recursmly Tnivartant P-recurston Theory

'We int¡oduce recursively invariant p-recursion theory as a new approach towards recursion theory on an arbitrary limit ordinal É. We follow Friedman and Sacks and call a subset of BB-recursively enumerable if it is.Xr-definable over Lu. Since Friedman-Sacks'notion of a p-finite set is not invariant under p-recursive permutations of p we turn to a different notion. Under all possible invariant ...

Syntactic recursion and theory-of-mind reasoning in agrammatic aphasia

This study investigates how aphasic impairment impinges on recursivity of language and theory-of-mind inferences. Results of linguistic tests showed that i aphasia syntactic recursion is substituted for theory-of-mind inferences on the base that linguistic system and theoryofmind type reasoning interact with one recursion modul in human mind.

Bounded Queries in Recursion Theory: A Survey

Abstracts of the invited speakers

s of the invited speakers Dag Normann, University of Oslo, Norway Revisiting Transfinite Types In this talk I will reconstruct spaces of countable and uncountable transfinite types, this time using limit spaces. This approach turns out to give a better access to internal concepts of computability for such spaces. The talk will be a report on ongoing research. This research is rooted in earlier ...

Applications of Classical Recursion Theory to Computer Science

Three applications oE intensional recursion theory to computer science are presented. Proof Lechn iqut.-.i are used, in some cases, as a criterion of appliciibiLity. The first example distinguishes various tormy of recursion as programming tools. A highly iccur-jivc proof of the famous speed up theorem from complexity theory is presented. The final application concerns the synthesis of programs...