相关论文: Interpreting the arithmetic in Thompson's group F
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
In 1968, John Thompson proved that a finite group G is solvable if and only if every 2-generator subgroup of G is solvable. In this paper, we prove that solvability of a finite group G is guaranteed by a seemingly weaker condition: G is…
In our article in MCU'2013 we state the the Domino problem is undecidable for all Baumslag-Solitar groups $BS(m,n)$, and claim that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for…
We prove that in a continuous $\aleph_0$-stable theory every type-definable group is definable. The two main ingredients in the proof are: \begin{enumerate} \item Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from…
In this paper it is proved that the group $F\left(\frac32\right)$, a Thompson-style group with breaks in $\mathbb{Z}\left[\frac16\right]$ but whose slopes are restricted only to powers of $\frac32$, is finitely generated, with a generating…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
The $F$-triangle is a refined face count for the generalised cluster complex of Fomin and Reading. We compute the $F$-triangle explicitly for all irreducible finite root systems. Furthermore, we use these results to partially prove the…
We prove a homological stability theorem for families of discrete groups (e.g. mapping class groups, automorphism groups of free groups, braid groups) with coefficients in a sequence of irreducible algebraic representations of arithmetic…
We show that a large class of divisible abelian $\ell$-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the…
Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…
We prove that Richard Thompson's group F is not minimally almost convex with respect to the two standard generators. This improves upon a recent result of S. Cleary and J. Taback. We make use of the forest diagrams for elements of F…
We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a…
We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.
We investigate the cogrowth and distribution of geodesics in R. Thompson's group $F$.
We introduce a refinement of bounded cohomology and prove that the suitable comparison homomorphisms vanish for an amenable group. We investigate in this context Thompson's group F and provide further evidence towards its amenability. We…
We prove, assuming resolution of singularities in positive characteristic, an analogue of Siegel's theorem on sum of squares in positive characteristic. The method of proof combines techniques from central simple algebras with model theory…
We investigate systems of equations and the first-order theory of one-relator monoids. We describe a family $\mathcal{F}$ of one-relator monoids of the form $\langle A\mid w=1\rangle$ where for each monoid $M$ in $\mathcal{F}$, the…
We show that there cannot be any algorithm that for a given nondeterministic polynomial-time Turing machine determinates whether or not the language recognized by this machine belongs to P
We define the notion of computability of F{\o}lner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has…
We study the Diophantine problem (decidability of finite systems of equations) in different classes of finitely generated solvable groups (nilpotent, polycyclic, metabelian, free solvable, etc), which satisfy some natural…