An autostable 2 nilpotent group with no Scott family of finitary formulas.
An intensional approach to questions
Boolean algebras with finite families of computable automorphisms.
Complexity of some natural problems in automatic structures.
Computability in special models.
Computable categoricity versus relative computable categoricity
We study the notion of computable categoricity of computable structures, comparing it especially to the notion of relative computable categoricity and its relativizations. We show that every 1 decidable computably categorical structure is relatively Δ⁰₂ categorical. We study the complexity of various index sets associated with computable categoricity and relative computable categoricity. We also introduce and study a variation of relative computable categoricity, comparing it to both computable...
Computable families of superatomic Boolean algebras.
Computable structures and operations on the space of continuous functions
We use ideas and machinery of effective algebra to investigate computable structures on the space C[0,1] of continuous functions on the unit interval. We show that (C[0,1],sup) has infinitely many computable structures non-equivalent up to a computable isometry. We also investigate if the usual operations on C[0,1] are necessarily computable in every computable structure on C[0,1]. Among other results, we show that there is a computable structure on C[0,1] which computes + and the scalar multiplication,...
Computably rigid models with enumerable submodels.
Elementary submodels of parametrizable models.
Estimation of the algorithmic complexity of classes of computable models.
Groups of automatic automorphisms of some automatic structures.
Hyperarithmetical Boolean algebras with a distinguished ideal.
Index sets of classes of automatic structures.
Index sets of classes of automatic structures.
Index sets of decidable models.
On a hierarchy of groups of computable automorphisms.
On a sufficient condition for strong constructivizability of atomic Boolean algebras.
On constructive nilpotent groups.
On constructivizability of the tensor product of modules.