Products in the category of apartness spaces
Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories.
Provability in arithmetic and a schema of Grzegorczyk
Provability in the alternative set theory
Quantum B-algebras
The concept of quantale was created in 1984 to develop a framework for non-commutative spaces and quantum mechanics with a view toward non-commutative logic. The logic of quantales and its algebraic semantics manifests itself in a class of partially ordered algebras with a pair of implicational operations recently introduced as quantum B-algebras. Implicational algebras like pseudo-effect algebras, generalized BL- or MV-algebras, partially ordered groups, pseudo-BCK algebras, residuated posets,...
Quantum coherent spaces and linear logic
Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that,...
Quantum coherent spaces and linear logic
Quantum Coherent Spaces were introduced by Girard as a quantum framework where to interpret the exponential-free fragment of Linear Logic. Aim of this paper is to extend Girard's interpretation to a subsystem of linear logic with bounded exponentials. We provide deduction rules for the bounded exponentials and, correspondingly, we introduce the novel notion of bounded exponentials of Quantum Coherent Spaces. We show that the latter provide a categorical model of our system. In order to do that,...
Ramified analysis and the minimal β-models of higher order arithmetics
Recursion in total functionals of finite type
Recursive Arithmetic of Skolem II.
Recursive metric spaces
Reduced Products Of Saturated Intuitionistic Theories
Reduced products of saturated intuitionistic theories.
Reducibilities of sets based on constructive functions of a real variable
Relatively constructible transitive models
Remarks on the structure of tt-degrees based on constructive measure theory
Representation of metamorphosis grammar in logic grammar: Proof trees and their lengths.
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.
Sätze über Determinanten und Anwendung derselben zum Beweise der Sätze von Pascal und Brianchon.