In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk Theorem, which deals with the case that R is a field (of any characteristic). Here we will show that for tameness over an Artinian ring, the Q-algebra assumption ...

This paper deals with a vector polynomial optimization problem over basic closed semi-algebraic set. By invoking some powerful tools from real geometry, we first introduce the concept called tangency varieties; obtain relationships of Palais–Smale condition, Cerami M-tameness, and properness related to considered problem, in which condition Mangasarian–Fromovitz constraint qualification at infi...

This is a survey of results of the profinite approach to decidability problems in the theory of finite semigroups.

In this paper we prove that, if V is a κ-tame pseudovariety which satisfies the pseudoidentity xyz = xyz, then the pseudovariety join LSl∨V is also κ-tame. Here, LSl denotes the pseudovariety of local semilattices and κ denotes the implicit signature consisting of the multiplication and the (ω − 1)-power. As a consequence, we deduce that LSl ∨V is decidable. In particular the joins LSl ∨ Ab, LS...

We show that ℶ(2LS(K))+ is the lower bound to Hanf numbers for length of order property and stability in stable abstract elementary classes (AECs). Our examples satisfy joint embedding property, no maximal model, (<ℵ0)-tameness but not necessarily amalgamation property. also define variations on syntactic properties insofar as it allows index set be linearly ordered rather than well-ordered. Co...