Transfinite inductions producing coanalytic sets

Transfinite interpolation over implicitly defined sets

In a general setting, the transfinite interpolation problem requires constructing a single function´Üµ that takes on the prescribed values and/or derivatives on some collection of point sets. The sets of points may contain isolated points, bounded or unbounded curves, as well as surfaces and regions of arbitrary topology. All such closed semi-analytic sets may be represented implicitly by real ...

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...