There are basically two ways to view intuitionistic logic: as a philosophical‐foundational
issue in mathematics; or as a technical discipline within mathematical logic. Considering first …

Among these logics that deal with the familiar connectives and quantifiers two stand out as
having a solid philosophical-mathematical justification. On the one hand there is a classical …

The first draft of this paper was conceived as a sort of survey of the conceptual analysis of
choice sequences in historical perspective; it was hoped this would adequately refute some …

This research is the result of a fruitful connection and provides a sign-cant link between two
topics of a logical and philosophical enquiry. It tries to provide a solution to the problem of …

Time-progressing expressions, ie, expressions that compute to different values over time
such as Brouwerian choice sequences or reference cells, are a common feature in many …

Markov's Principle (MP) is a central principle in constructive mathematics, nowadays most
commonly stated as follows [7, 8, 46]:∀ 𝑓: N→ B.¬¬(∃ 𝑛. 𝑓𝑛= true)→∃ 𝑛. 𝑓𝑛= true It …

We construct a continuous model of Gödel's system T and its logic HA ω in which all
functions from the Cantor space 2 ℕ to the natural numbers are uniformly continuous. Our …

We identify yet another category equivalent to that of Kleene–Kreisel continuous functionals.
Reasoning constructively and predicatively, all functions from the Cantor space to the …

We give a general theory of the logic of potentially infinite objects, derived from a theory of
meaning for statements concerning these objects. The paper has two main parts which may …

Extending Martín Escardó's effectful forcing technique, we give a new proof of a well-known
result: Brouwer's monotone bar theorem holds for any bar that can be realized by a …