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...

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...

We are interested in the question whether the models induced by the infinitary lambda calculus are orderable, that is whether they have a partial order with a least element making the context operators monotone. The first natural candidate is the prefix relation: a prefix of a term is obtained by replacing some subterms by ⊥. We prove that six models induced by the infinitary lambda calculus (w...