A henselian valued field K is called a tame field if its algebraic closure K̃ is a tame extension, that is, the ramification field of the normal extension K̃|K is algebraically closed. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We develop the algebraic theory of tame fields and then prove Ax–Kochen– Ershov Principles for tame fields. This leads to model compl...

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...

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 ...

Let k be a p-adic field of characteristic zero and residue characteristic p. Let G be the group of k-points of a connected reductive group G defined over k. In [38], Yu gives a fairly general construction of supercuspidal representations of G in a certain tame situation. In this paper, subject to some hypotheses on G and k, we prove that all supercuspidal representations arise through his const...

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-...

In this note we settle a question posed by Hobby and McKenzie in [2] on the nature of locally finite equational classes which satisfy some nontrivial congruence identity. We settle problem #14 from [2] by exhibiting a locally finite equational class V which omits types 1 and 5 and which satisfies some non-trivial congruence identity, but which contains a finite algebra having a type 4 minimal s...

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 metr...

Tame is a new event-based system for managing concurrency in network applications. Code written with Tame abstractions does not suffer from the “stackripping” problem associated with other event libraries. Like threaded code, tamed code uses standard control flow, automatically-managed local variables, and modular interfaces between callers and callees. Tame’s implementation consists of C++ lib...