On Intuitionistic Sentential Connectives I.
On Kalmar's consistency proof and a generalization of the notion of ...-consistency.
On local proof restrictions for strong theories [Book]
On necessary but not-sufficient conditions.
On non-tabular -pre-complete classes of formulas in the propositional provability logic.
On normalization of proofs in set theory [Book]
On quasi-antiorder in semigroups
On rational solution of the state equation of a finite automaton.
On recursive measure of classes of recursive sets
On Regular Anti-congruence in Anti-ordered Semigroups
On separation axioms in intuitionistic topological spaces.
On sequent calculi for intuitionistic propositional logic
The well-known Dyckoff's 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidability of this calculus is given. An upper bound on the depth of a Kripke counter-model is obtained.
On the axiomatisation of Boolean categories with and without medial.
On the complexity of computable real sequences
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 Quantifier of Limiting Realizability
On the structure of intuitionistic algebras with relational probabilities.
Trillas ([1]) has defined a relational probability on an intuitionistic algebra and has given its basic properties. The main results of this paper are two. The first one says that a relational probability on a intuitionistic algebra defines a congruence such that the quotient is a Boolean algebra. The second one shows that relational probabilities are, in most cases, extensions of conditional probabilities on Boolean algebras.
On the weak pigeonhole principle
We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of the Ramsey theorem. In particular, we link the proof complexities of these two principles. Further we give lower bounds to the width of resolution proofs and to the size of (extensions of) tree-like resolution proofs of the Ramsey theorem. We establish a connection between provability of WPHP in fragments of bounded arithmetic and cryptographic assumptions (the existence...
On two Classical Results in the First Order Logic