In this note we give a sufficient condition that a 2-cell or disk in E3 be pierced by a tame arc at each point of its interior. This condition is simply that each arc in the disk be tame. The method of proof leans heavily upon some results of Bing and Moise as well as upon a theorem on the union of tame disks by one of the present authors. Remark. Lemma 7 of [2] asserts that if two tame disks i...

If every finitely generated subalgebra of an algebra A has a property P , then A is said to have P as a local property. In this paper we study classes L(K) and M(K), where K is a class of unary algebras, L(K) consists of all algebras such that every finitely generated subalgebra is in K, and M(K) is the class of all algebras with every monogenic subalgebra in K. In particular, the cases where K...

The implicit signature κ consists of the multiplication and the (ω − 1)-power. We describe a procedure to transform each κ-term over a finite alphabet A into a certain canonical form and show that different canonical forms have different interpretations over some finite semigroup. The procedure of construction of the canonical forms, which is inspired in McCammond’s normal form algorithm for ω-...

The tame flows are “nice” flows on “nice” spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow Φ : R×X → X on pfaffian set X is tame if the graph of Φ is a pfaffian subset of R×X×X . Any compact tame set admits plenty tame flows. We prove that the flow determined by the gradient of a generic real analytic function with respect to a generic real analytic metric ...

— This article defines the notion of hyperdecidability for a class offinlte semigroups, which is closely connected to the notion of decidability. It then proves that the pseudovariety J of J-trivial semigroups is hyperdecidable.

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. This results from the main theorem of this paper, which asserts that an automorphism in any dimension n is stably tame if said condition holds point-wise over SpecR. A key element in the proof is a theorem which yields the following corollary: Over an Artinian ring A all two-...

Given a regular language L, we effectively construct unary semigroup that recognizes the topological closure of L in free relative to variety semigroups generated by pseudovariety R all finite R-trivial semigroups. In particular, obtain new effective solution separation problem languages R-languages.