Reconstruction results give conditions under which the abstract group structure of the automorphism group Aut(M) of an ω-categorical structure M determines the topology on Aut(M), and hence determines M up to biinterpretability, by [1]; they can also give conditions under which the abstract group Aut(M) determines the permutation group 〈Aut(M),M〉, so determines M up to bi-definability. One such...

Given a subset of X ⊆ ℝn we can associate with every point x ∈ vector space V maximal dimension the property that for some ball centered at x, coincides inside union lines parallel to V. A is singular if has 0. In an earlier paper proved 〈ℝ, +, <, ℤ〉-definable relation 1〉-definable and only number points finite rational section 〈R, 1〉-definable, where set obtained from by fixing component va...

The ability to rewrite defined ontological entities into syntactically different, but semantically equivalent forms is an important property of Definability. While rewriting has been extensively studied, the practical applicability of currently existing methods is limited, as they are bounded to particular Description Logics (DLs), and they often present only theoretical results. Moreover, thes...

More than 40 years the correspondence between modal logic and first-order logic, when they are interpreted in relational structures, is on the main stream of the investigations of many modal logicians. The most interesting in this direction is a series of results on modal and first-order definability proved by Chagrova in the 1990s. In particular, from them it follows the undecidability of both...