Related papers: Notes on axiomatising Hurkens's Paradox

We prove an extensionality theorem for the "type-in-type" dependent type theory with Sigma-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the free term model of type theory.

This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a…

The Frankl conjecture (called also union-closed sets conjecture) is one of the famous unsolved conjectures in combinatorics of finite sets. In this short note, we introduce and to some extent justify some variants of the Frankl conjecture.

We survey the classical results of the Dirichlet Approximation Theorem.

Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation…

We prove that in theories without the tree property of the second kind (which include dependent and simple theories) forking and dividing over models are the same, and in fact over any extension base. As an application we show that…

Moores Paradox is a test case for any formal theory of belief. In Knowledge and Belief, Hintikka developed a multimodal logic for statements that express sentences containing the epistemic notions of knowledge and belief. His account…

We extend Stein's method to include dependence with respect to an auxiliary random variable, for conditional laws for which Stein's characterizations do exist.

We reduce the Nowicki conjecture on the Weitzenb\"ock derivation of polynomial algebras to well-known problem of the classical invariant theory.

We study the properties, in particular termination, of dependent types systems for lambda calculus and rewriting.

We investigate Hindman- and Owings-type Ramsey-theoretic statements in Zermelo-Fraenkel set theory without the Axiom of Choice, with some occasional extra assumptions (such as the Axiom of Dependent Choice and/or the Axiom of Determinacy).…

We define an analogue of the Fox derivatives for differential polynomial algebras and give a criterion for differential algebraic dependence of a finite system of elements. In particular, we prove that differential algebraic dependence of a…

We report the results of our empirical investigations on the Bateman-Horn conjecture. This conjecture, in its commonly known form, produces rather large deviations when the polynomials involved are not monic. We propose a modified version…

A combinatorial group-theoretic hypothesis is presented that serves as a necessary and sufficient condition for a union of connected Cockcroft two-complexes to be Cockcroft. This hypothesis has a component that can be expressed in terms of…

In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.

We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the…

We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…

We study the Wick symbol of a solution of the time dependent Hartree Fock equation, under weaker hypotheses than those needed for the Weyl symbol in the first paper with thesame title. With similar, we prove some kind of Ehrenfest theorem…

In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.

This paper is concerned with the axiomatic basis of structures within Hypercompositional Algebra. It is proven that the axioms employed in the definition of numerous hypercompositional structures lack independence. Accordingly, novel…