Transfinite extent

Transfinite Equations in Transfinite Strings

Transfinite Diameter

The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...

Transfinite rewriting

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.

Transfinite Cryptography

Let assume that Alice, Bob, and Charlie, the three classical people of cryptography are not limited anymore to perform a finite number of computations on real computers, but are limited to α computations and to α bits of memory, where α is a fixed infinite cardinal. For example α = א0 (the countable cardinal, i.e. the cardinal of N the set of integers), or α = C (the cardinal of the set R of re...

Rewriting Transfinite Terms

We define rewriting over terms with positions of transfinite length.