Related papers: The existence of a near-unanimity function is deci…

We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.

We prove that it is decidable if a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable substructure result for simple permutations: every sufficiently long simple permutation contains…

Necessary and sufficient conditions for the solvability of boundary value problems for a family of functional differential equations with a non-integrable singularity are obtained.

An interaction is a certain symmetric graph that describes the possible transition of states of adjacent sites of large-scale interacting systems. In the series of studies Bannai-Kametani-Sasada arXiv:2009.04699, Bannai-Sasada…

We give an elementary proof of a somewhat curious result, namely, that deciding whether a convex function is self-concordant is in general an intractable problem.

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…

We prove the undecidability of determining whether a Turing machine yields an eventually periodic trajectory. From this, we deduce the undecidability of orbit finiteness in the polynomial dynamical system on infinite tuples of integers.

The main result is the following: Let X be a finite set and D be a non empty family of choice functions for (X choose 2) closed under permutation of X. Then the following conditions are equivalent: (A) for any choice function c on (X choose…

We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…

We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games.

It is undecidable whether the language recognized by a probabilistic finite automaton is empty. Several other undecidability results, in particular regarding problems about matrix products, are based on this important theorem. We present…

We devise a condition strictly between the existence of an $n$-ary and an $n{+}1$-ary near-unanimity term. We evaluate exactly the distributivity and modularity levels implied by such a condition.

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding…

In this article we prove results about finite soluble groups that act with fixity 2 or 3.

We prove that any finite set $F\subset {\mathbb{Z}^2}$ that tiles ${\mathbb{Z}^2}$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\mathbb{Z}^2}$ is decidable.

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…

We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying…

In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and develop a comparison test for such series which can be used even…