For every countable ordinal number ?, we construct a metric space X? whose transfinite asymptotic dimension and complementary-finite are both ?.

We show that non-collapsing orthogonal term rewriting systems do not have the transfinite Church-Rosser property in the setting of Cauchy convergence. In addition, we show that for (a transfinite version of) the Parallel Moves Lemma to hold, any definition of residual for Cauchy convergent rewriting must either part with a number of fundamental properties enjoyed by rewriting systems in the fin...

This is a brief survey of the use of transfinite induction in metric fixed-point theory. Among the results discussed in some detail is the author’s 1989 result on directionally nonexpansive mappings (which is somewhat sharpened), a result of Kulesza and Lim giving conditions when countable compactness implies compactness, a recent inwardness result for contractions due to Lim, and a recent exte...

We survey the basic concepts and properties of transfinite rewriting for orthogonal term rewrite systems, lambda calculus, higher-order rewrite systems, and abstract rewrite systems.

This paper examines the consistency of ω-order by means of a supertask that functions as a supertrap for the assumed existence of ω-ordered collections, which are simultaneously complete (as is required by the Actual infinity) and uncompletable (because no last element completes them). As Cantor himself proved [2], [3], ω-order is a formal consequence of assuming the existence of denumerable se...

“Bricolage”, a multidisciplinary term used extensively in visual arts, anthropology and cultural studies, refers to a creation that borrows elements from a diverse range of existing designs. The term is applied here to describe CSALF-Q, a new automatic 2D quad meshing algorithm that combines the strengths of recursive subdivision, loop-paving and transfinite interpolation to generate surface me...

This paper presents a new super-element with twelve degrees of freedom for latticed columns. This elements is developed such that it behaves, with an acceptable approximation, in the same manner as a reference model does. The reference model is constructed by using many Solid elements. The cross section area, moments of inertia, shear coefficient and torsoinal rigidity of the developed new elem...

In a recent paper,f André Gleyzal has constructed ordered fields consisting of certain "transfinite real numbers" and has established the interesting result that any ordered field can be considered as a subfield of one of these transfinite fields. These fields prove to be identical with fields of formal power series in which the exponents are allowed to range over a suitable ordered abelian gro...