This article studies the function of Copular Predicate Constructions in everyday English conversation. We compare predicate adjective constructions (PA) and with a nominal containing an (PAN). ask whether attributive or presence noun PAN leads to difference two constructions. propose that most cases determines construction, leading many parallels usage between PA A comparison (PN), contrast, sh...

In 1958 Gödel published his Dialectica interpretation, which reduces classical arithmetic to a quantifier-free theory T axiomatizing the primitive recursive functionals of finite type. Here we extend Gödel’s T to theories Pn of “predicative” functionals, which are defined using MartinLöf’s universes of transfinite types. We then extend Gödel’s interpretation to the theories of arithmetic induct...

Formalized mathematics and mathematical knowledge management (MKM) are extremely fruitful and quickly expanding fields of research at the intersection of mathematics and computer science. The declared goal of these fields is to develop computerized systems that effectively represent all important mathematical knowledge and techniques, while conforming to the highest standards of mathematical ri...

3 The main hierarchy 2 1 Contextual categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Π-contextual categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3 Impredicative Π-universe structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 Predicative Π-universe structures. . . . . . . . . . . . . . . . . . . . . . . . . ...

Several variations on the definition of a Formal Topology exist in the literature. They differ on how they express convergence, the formal property corresponding to the fact that open subsets are closed under finite intersections. We introduce a general notion of convergence of which any previous definition is a special case. This leads to a predicative presentation and inductive generation of ...

We give geometric characterisations of patch and Lawson topologies in the context of predicative point-free topology using the constructive notion of located subset. We present the patch topology of a stably locally compact formal topology by a geometric theory whose models are the points of the given topology that are located, and the Lawson topology of a continuous lattice by a geometric theo...