CDMTCS Research Report Series Another Example of Higher Order Randomness

CDMTCS Research Report Series Higher Randomness Notions and Their Lowness Properties

We study randomness notions given by higher recursion theory, establishing the relationships Π1-randomness ⊂ Π1-Martin-Löf randomness ⊂ ∆1randomness = ∆1-Martin-Löf randomness. We characterize the set of reals that are low for ∆1 randomness as precisely those that are ∆1 -traceable. We prove that there is a perfect set of such reals.

Cdmtcs Research Report Series on Hypersimple Sets and Chaitin Complexity on Hypersimple Sets and Chaitin Complexity

In this paper we study some computability theoretic properties of two notions of randomness for nite strings: randomness based on the blank-endmarker complexity measure and Chaitin randomness based on the self-delimiting complexity measure. For example, we nd the position of RAND and RAND at the same level in the scale of immunity notions by proving that both of them are not hyperimmune sets. A...

Cdmtcs Research Report Series Computable Kripke Models and Intermediate Logics

We introduce e ectiveness considerations into model theory of intuitionistic logic. We investigate e ectiveness of completeness (by Kripke) results for intermediate logics such as for example, intuitionistic logic, classical logic, constant domain logic, directed frames logic, Dummett's logic, etc.

CDMTCS Research Report Series Scott Families and Computably Categorical Structures

Cdmtcs Research Report Series Randomness Spaces Randomness Spaces

Martin-Lof de ned in nite random sequences over a nite alphabet via randomness tests which describe sets having measure zero in a constructive sense. In this paper this concept is generalized to separable topological spaces with a measure, following a suggestion of Zvonkin and Levin. After studying basic results and constructions for such randomness spaces a general invariance result is proved...