A generalization of elementary formal systems
A version of the ...1-reflection principle for CFA provable in PRA.
Axiomatizability of second order arithmetic with ω-rule
Beweistheoretische Abgrenzung von Teilsystemen der Analysis.
Choice sequences and reduction processes.
Deductive systems of BCK-algebras
In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator of a deductive system is the the pseudocomplement of . These results are more general than that the similar results given by M. Kondo in [7].
Definable quantifiers in second order arithmetic and elementary extensions of ω-models [Book]
Geometric and higher order logic in terms of abstract Stone duality.
Indécidabilité de la théorie des anneaux de séries formelles à plusieurs indéterminées
König's Lemma, the ...-rule and primitive recursive arithmetic.
Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume.
Non standard interpretations of higher order theories
Non-finitizability of a weak second-order theory
O druhém Hilbertově problému (Otázka bezespornosti aritmetiky)
On a unification problem related to Kreisel's conjecture
On interpretability in theories containing arithmetic. II.
Ramified analysis and the minimal β-models of higher order arithmetics
Relatively constructible transitive models
Representations of Reals in Reverse Mathematics
Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in RCA₀. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKL₀ or ACA₀.
Reverse mathematics of some topics from algorithmic graph theory
This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.