A concurrent object is an object that can be concurrently accessed by several processes. Two well known consistency criteria for such objects are atomic consistency (also called linearizability) and sequential consistency. Both criteria require that all the operations on all the concurrent objects be totally ordered in such a way that each read operation obtains the last value written into the ...

Given an ergodic probability measure preserving dynamical system Γ y (X,μ), where Γ is a finitely generated countable group, we show that the asymptotic growth of the number of finite models for the dynamics, in the sense of sofic approximation, is an invariant of orbit equivalence. We then prove an additivity formula for free products of orbit structures with amenable (possibly trivial) amalga...

Infinite fields are not finitely generated rings. Similar question is considered for further algebraic structures, mainly commutative semirings. In this case, purely algebraic methods fail and topological properties of integral lattice points turn out to be useful. We prove that a commutative semiring that is a group with respect to multiplication, can be two-generated only if it belongs to the...

In [Ann. Math. 190 (2019), 657-661], James Hyde presented the first example of non-left-orderable, finitely generated subgroup $\mathrm{Homeo}(D,\partial D)$, group homeomorphisms disk fixing boundary. This implies that D)$ itself is not left-orderable. We revisit construction, and present a slightly different proof purely dynamical flavor, avoiding direct references to properties left-orders. ...

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by balls to quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated groups. Inspired work Benjamini and Schramm, we show under such maps, some kind of dimension increases: exponent volume growth nilpotent groups, the ideal boundary hyperbo...

We investigate the Hasse principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets discrete valuations. Over purely transcendental fields that satisfy property $\mathscr{A}_i(2)$ some $i$, we find numerous counterexamples principle a relatively small set For $K$ transcendence degree $r$ an algebraically closed characteristic $\...

A Puiseux monoid is an additive submonoid of the nonnegative rational numbers. If M a monoid, then question whether each nonunit element can be written as sum irreducible elements (that is, atomic) surprisingly difficult. For instance, although various techniques have been developed over past few years to identify subclasses monoids that are atomic, no general characterization such known. Here ...

There are structures A which can be described up to isomorphism by a single sentence φ (in some logic), that is, B |= φ ⇐⇒ B ∼= A for all B. If the structure A is finite, then φ can be taken as a first-order sentence. We want to have φ as succinct as possible. (Therefore, a sentence ψ in some non-first-order logic could be a better choice.) 1 Atomic Complexity of structures Let A = 〈A,S〉 be a s...

We use coalgebraic methods to describe finitely generated free Heyting algebras. Heyting algebras are axiomatized by rank 0-1 axioms. In the process of constructing free Heyting algebras we first apply existing methods to weak Heyting algebras—the rank 1 reducts of Heyting algebras—and then adjust them to the mixed rank 0-1 axioms. On the negative side, our work shows that one cannot use arbitr...

The interest of investigating combinations of logics has a philosophical side, a purely logic-theoretical side and promising applicational interests. This paper concentrates on the logic-theoretical side and studies some general methods for combination and decomposition, taking into account that the general idea of combining logics requires methods not only for building new logics, but also for...