It is shown that the categories of R-coalgebras for a commutative unital ring R and the category of A-corings for some R-algebra A as well as their respective categories of comodules are locally presentable.

Bumagin–Wise posed the question of whether every countable group can be realised as the outer automorphism group of a finitely generated, residually finite group. We give a partial answer to this problem for recursively presentable groups.

The Hahn spin-echo (HSE)-based BOLD effect at high magnetic fields is expected to provide functional images that originate exclusively from the microvasculature. The blood contribution that dominates HSE BOLD contrast at low magnetic fields (e.g., 1.5 T), and degrades specificity, is highly attenuated at high fields because the apparent T(2) of venous blood in an HSE experiment decreases quadra...

We investigate in this paper a certain notion of comparison between infinite words. In a general way, if M is a model of computation (e.g. Turing machines) and C a class of objects (e.g. languages), the complexity of an infinite word α can be measured with respect to the objects from C that are presentable with machines from M using α as an oracle. In our case, the model M is finite automata an...

Two ways of describing a group are considered. 1. A group is finiteautomaton presentable if its elements can be represented by strings over a finite alphabet, in such a way that the set of representing strings and the group operation can be recognized by finite automata. 2. An infinite f.g. group is quasi-finitely axiomatizable if there is a description consisting of a single first-order senten...

We study the relationship between a computably enumerable real and its presentations. A set A presents a computably enumerable real α if A is a computably enumerable prefix-free set of strings such that α = ∑ σ∈A 2 −|σ|. Note that ∑ σ∈A 2 −|σ| is precisely the measure of the set of reals that have a string in A as an initial segment. So we will simply abbreviate ∑ σ∈A 2 −|σ| by μ(A). It is know...

Filling length measures the length of the contracting closed loops in a null-homotopy. The filling length function of Gromov for a finitely presented group measures the filling length as a function of length of edge-loops in the Cayley 2-complex. We give a bound on the filling length function in terms of the log of an isoperimetric function multiplied by a (simultaneously realisable) isodiametr...