Some very difficult questions in finite geometry (for example, concerning ovoids, spreads, and extensions) have fairly trivial resolutions in the infinite case, by standard transfinite induction. We give some old and new results of this kind, and a number of open questions. The paper is expository in nature, and is intended to illustrate the technique rather than give the most general applicati...

We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating given equivalence relation. investigate those.

We apply Mints’ technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.

We present a simple-to-state, abstract computational problem, whose solution implies the 1consistency of various systems of predicative Analysis and offers a way of extracting witnesses from classical proofs. In order to state the problem, we formulate the concept of transfinite update procedure, which extends Avigad’s notion of update procedure to the transfinite and can be seen as an axiomati...

This paper studies mathematically some special kinds of transfinite trace semantics and investigates program slicing w.r.t. these semantics. Several general facts about slicing, which hold for a wide class of programming languages and their transfinite semantics, are proven. The principal part of the work is done on control flow graphs keeping the treatment abstracted from any concrete programm...