The theory of locales [23] has a twofold interplay with intuitionistic mathematics: first of all, the internal logic of toposes and intuitionistic set theories provide suitable settings for the development of the theory of locales [24], and secondly, the notion of a locale determines two important forms of toposes and of interpretations for intuitionistic set theories, namely localic toposes [2...

The study investigated the potential for facial electromyography (EMG) to be used as a clinical tool for measuring the responses of children to pleasant and unpleasant smell and taste stimuli. Responses in the zygomaticus major and levator labii muscles to 4 odorants and 4 tastants were recorded from 34 children aged 6-9 years. The results indicated that EMG activities in the 2 muscles discrimi...

In this paper the machinery and results developed in [Awodey et al, 2004] are extended to the study of constructive set theories. Specifically, we introduce two constructive set theories BCST and CST and prove that they are sound and complete with respect to models in categories with certain structure. Specifically, basic categories of classes and categories of classes are axiomatized and shown...

The subject of this work is quantum predicative programming — the development of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming methodology. Our work is based on probabilistic predicative programming, a recent generalisation of the well-established predicative programming. It supports the styl...

In this paper, we characterize the strength of the predicative Frege hierarchy, PV, introduced by John Burgess in his book [Bur05]. We show that PV and Q + con(Q) are mutually interpretable. It follows that PV := PV is mutually interpretable with Q. This fact was proved earlier by Mihai Ganea in [Gan06] using a different proof. Another consequence of the our main result is that PV is mutually i...

A predicative semantics is a mapping of programs to predicates These pred icates characterize sets of acceptable observations The presence of time in the observations makes the obvious weakest xed point semantics of itera tive constructs unacceptable This paper proposes an alternative We will see that this alternative semantics is monotone and implementable feasible Fi nally a programming theor...

In 1990, W. Hugh Woodin introduced Omega-logic as an approach to truth in the universe of all sets inspired by recent work on large cardinals and determinacy. In Omega-logic statements are valid if, roughly, they hold in every forcing extension of the universe, or its sufficiently rich initial segments. Thus, Omega-logic is the logic of generic absoluteness. In this short course we will start w...

In this article we develop a Mahlo universe in Explicit Mathematics using extended predicative methods. Our approach differs from the usual construction in type theory, where the Mahlo universe has a constructor that refers to all total functions from families of sets in the Mahlo universe into itself; such a construction is, in the absence of a further analysis, impredicative. By extended pred...