In this document I will outline a couple of recent developments, due to Joel Hamkins, Philip Welch and myself, in the theory of infinite-time Turing machines. These results were obtained with the idea of extending the scope of the study of Borel equivalence relations, an area of descriptive set theory. I will introduce the most basic aspects of Borel equivalence relations, and show how infinite...

Abstract Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide fix: show that is maximal abstract satisfying weak form the isomorphism property (suitable for identity-free languages and studied in [11]), Löwenheim–Skolem property, compactness. Furthermore, compactness can be replaced by ...

This work deals with the specification and the verification of concurrent systems. Our goal is to exploit an implementable model, namely the maximality -based labelled transition system, which permits expressing true-concurrency in a natural way without splitting actions on their start and end events. To do this, we give an operational semantics to build maximality-based labelled transition sys...

A choice correspondence is weak justified if a non-chosen alternative is dominated by any other obtainable alternative, and for each discarded alternative there is some chosen alternative which dominates it. This definition allows us to build a connection between the behavioral property expressed by the weak axiom of revealed non-inferiority and a weak form of maximality. It is weaker than the ...