On the form of functions which preserve regressive isols
On the Goldbach conjecture and the consistency of general recursive arithemetic.
On the hierarchies of Δ20-real numbers
A real number x is called Δ20 if its binary expansion corresponds to a Δ20-set of natural numbers. Such reals are just the limits of computable sequences of rational numbers and hence also called computably approximable. Depending on how fast the sequences converge, Δ20-reals have different levels of effectiveness. This leads to various hierarchies of Δ20 reals. In this survey paper we summarize several recent developments related to such kind of hierarchies shown by the author and his collaborators. ...
On the index sets of -subsets of the real numbers.
On the lengths of bad sequences of monomial ideals over polynomial rings
We give bad (with respect to the reverse inclusion ordering) sequences of monomial ideals in two variables with Ackermannian lengths and extend this to multiple recursive lengths for more variables.
On the problem of finite signature.
On the reducibility of the index sets of families of general recursive functions.
On the relation of -reducibility between admissible sets.
On the resemblance and recursive isomorphism types of partial recursive functions.
On the restricted equivalence for subclasses of propositional logic
On the topological complexity of infinitary rational relations
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [20].
On the Topological Complexity of Infinitary Rational Relations
We prove in this paper that there exists some infinitary rational relations which are analytic but non Borel sets, giving an answer to a question of Simonnet [20].
On two complete sets in the analytical and the arithmetical hierarchies.
On two problems of mice
Optimal bounds for ordinal comparison maps.
Paradis terrestre dans l'automate cellulaire de Conway
Parametric inductive definitions and recursive operators over the continuum
Partial conservativity revisited
Partial countable and finite functionals.
Polynomial time bounded truth-table reducibilities to padded sets
We study bounded truth-table reducibilities to sets of small information content called padded (a set is in the class of all -padded sets, if it is a subset of ). This is a continuation of the research of reducibilities to sparse and tally sets that were studied in many previous papers (for a good survey see [HOW1]). We show necessary and sufficient conditions to collapse and separate classes of bounded truth-table reducibilities to padded sets. We prove that depending on two properties of a...