Related papers: Implicative algebras II: completeness w.r.t. Set-b…
Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface $S$ endowed with a holomorphic symplectic form $\omega$ and a projection onto $\mathbb{C}$. We provide a full…
A formalisation of G\"odel's incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows {\'S}wierczkowski…
Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…
A complete proof is given of relative interpretability of Adjunctive Set Theory with Extensionality in an elementary concatenation theory.
We prove that for any set $F$ of $n\ge 2$ pairwise disjoint open convex sets in $\mathbb{R}^3$, the connected components of the set of lines intersecting every member of $F$ are contractible. The same result holds for directed lines.
We prove that any analytic set in $\C^n$ with a unique tangent cone at infinity is an algebraic set. We prove that the degree of a complex algebraic set in $\C^n$, which is Lipschitz normally embedded at infinity, is equal to the degree of…
We prove that every real algebraic action on a smooth real algebraic variety has a prolongation with a "moving frame".
We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative…
We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…
In this paper we investigate classifications of all (transposed) Poisson algebras of the associated associative null-filiform algebra
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
We prove that all ($\alpha$-$\beta$)-shifts with $0\le \alpha<1$ and $\beta>2$ are saturated, that is, for any invariant measure, the topological entropy of the set of generic points coincides with the metric entropy.
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
We give a complete classification of (n+2)-dimensional n-Lie algebras over an algebraically closed field of characteristic $2$, and provide a isomorphic criterion theorem of (n+2)-dimensional n-Lie algebras.
Several results about the union-closed sets conjecture are presented.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
Under the prime-tuple hypothesis, the set of signed primes is a sumset.
Exactly integrable systems connected to semisimple algebras of second rank with an arbitrary choice of grading are presented in explicit form. General solutions of these systems are expressed in terms of matrix elements of two fundamental…