On account of being governed by constructive logic, intuitionistic theories T often enjoy
various existence properties. The most common is the numerical existence property (NEP). It …

This thesis aims at exploring the scopes and limits of techniques for extracting programs
from proofs. We focus on constructive theories of inductive definitions and classical systems …

Intrinsically circular phenomena have come to the attention of researchers in differing fields
such as mathematical logic, computer science, artificial intelligence, linguistics, cognitive …

Ambiguity is a property of syntactic expressions which is ubiquitous in all informal languages—
natural, scientific and mathematical; the efficient use of language depends to an exceptional …

We study the notion of non-trivial elementary embeddings j from the set-theoretic universe,
V, to itself under the assumption that V satisfies various classical and intuitionistic set …

The paper investigates inaccessible set axioms and their consistency strength in
constructive set theory. In ZFC inaccessible sets are of the form V κ where κ is a strongly …

We investigate large set axioms defined in terms of elementary embeddings over
constructive set theories, focusing on IKP and CZF. Most previously studied large set …

The Anti-Foundation axiom, AFA, has turned out to be a versatile principle in set theory for
modelling a plethora of circular and self-referential phenomena. This paper explores …

After briefly discussing the concepts of predicativity, metapredicativity and impredicativity, we
turn to the notion of Mahloness as it is treated in various contexts. Afterwards the appropriate …

We present an extension of constructive Zermelo–Fraenkel set theory [2]. Constructive sets
are endowed with an applicative structure, which allows us to express several set theoretic …