7 papers
Categories with a Base of Computability
Luis Gambarte, Iosif Petrakis
The notion of a base of computability in a category was introduced as a tool to generate computability models, in the sense of Longley and Normann, from…
Constructive Stone representations for separated swap and Boolean algebras
Daniel Misselbeck-Wessel, Iosif Petrakis
Swap algebras generalise Bishop's complemented powerset as Boolean algebras generalise the powerset. Actually, all Boolean algebras are swap algebras. We prove constructively a Sto…
Orthocomplemented subspaces and partial projections on a Hilbert space
Iosif Petrakis
We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dime…
Coinductive well-foundedness
Iosif Petrakis
We introduce a coinductive version of the well-foundedness of N that is used in our proof within minimal logic of the constructive counterpart CLNP to the standard least number pri…
Strong negation in the theory of computable functionals TCF
Nils Köpp, Iosif Petrakis
We incorporate strong negation in the theory of computable functionals TCF, a common extension of Plotkin's PCF and Gödel's system , by defining simultaneously strong…
Topologies of open complemented subsets
Iosif Petrakis
We introduce cs-topologies, or topologies of open complemented subsets, as a new approach to constructive topology that preserves the duality between open and closed subsets of cla…