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We introduce Z-stability, a notion capturing the intuition that if a function f maps a metric space into a normed space and if the norm of f(x) is small, then x is close to a zero of f. Working in Bishops constructive setting, we first study pointwi
We show that numerous distinctive concepts of constructive mathematics arise automatically from an antithesis translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented sub
We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any presheaf model
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
The variety generated by the Brandt semigroup ${bf B}_2$ can be defined within the variety generated by the semigroup ${bf A}_2$ by the single identity $x^2y^2approx y^2x^2$. Edmond Lee asked whether or not the same is true for the monoids ${bf B}_2^
These are the lecture notes of an introductory course on ordinal analysis. Our selection of topics is guided by the aim to give a complete and direct proof of a mathematical independence result: Kruskals theorem for binary trees is unprovable in cons