Deep learning is moving towards increasingly sophisticated optimization objectives that
employ higher-order functions, such as integration, continuous optimization, and root …

Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and
intuitionistic logic, has had profound effects on a number of branches of mathematical logic …

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 …

A new foundation for constructive nonstandard analysis is presented. It is based on an
extension of a sheaf-theoretic model of nonstandard arithmetic due to I. Moerdijk. The model …

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 …

The ALEA Coq library formalizes measure theory based on a variant of the Giry monad on
the category of sets. This enables the interpretation of a probabilistic programming language …

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 …

Derived rules for predicative set theory: An application of sheaves Page 1 Annals of Pure and
Applied Logic 163 (2012) 1367–1383 Contents lists available at SciVerse ScienceDirect …

In the late 1960s, Dana Scott first showed how the Stone-Tarski topological interpretation of
Heyting's calculus could be extended to model intuitionistic analysis; in particular Brouwer's …

In constructive algebra one cannot in general decide the irreducibility of a polynomial over a
field K. This poses some problems to showing the existence of the algebraic closure of K …