Related papers: On the Lambek-Moser Theorem

In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which combines an $L^p-L^\infty$-estimate with a weak $L^1$-estimate…

A rephrasing of Vogt's and Skof's version of the Ulam-Mazur theorem as a definability statement.

We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.

Most existing interpretable methods explain a black-box model in a post-hoc manner, which uses simpler models or data analysis techniques to interpret the predictions after the model is learned. However, they (a) may derive contradictory…

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown…

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

We give a new simpler proof of a theorem of Jayne and Rogers.

A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We…

It is well-known that the stable model structure on symmetric spectra cannot be transferred from the one on sequential spectra through the forgetful functor. We use the fibrant transfer theorem of Guetta--Moser--Sarazola--Verdugo to show it…

We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…

We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense…

Contrastive explanation methods go beyond transparency and address the contrastive aspect of explanations. Such explanations are emerging as an attractive option to provide actionable change to scenarios adversely impacted by classifiers'…

We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.