Related papers: Notes on axiomatising Hurkens's Paradox

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…

We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

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.

A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…

New cases of the multiplicity conjecture are considered.

A type analysable in one-based types in a simple theory is itself one-based.

One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…

In this paper, we show that Markov's principle is not derivable in dependent type theory with natural numbers and one universe. One way to prove this would be to remark that Markov's principle does not hold in a sheaf model of type theory…

Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

We generalize the quantum "pigeonhole paradox" to quantum paradoxes involving arbitrary types of particle relations, including orderings, functions and graphs.

The implication problem for the class of embedded dependencies is undecidable. However, this does not imply lackness of a proof procedure as exemplified by the chase algorithm. In this paper we present a complete axiomatization of embedded…

It is shown that the "twin paradox" arises from comparing unlike entities, namely perceived intervals with eigenintervals. When this lacuna is closed, it is seen that there is no twin paradox and that eigentime can serve as the independent…

We prove that an innocent looking inequality implies the Riemann Hypothesis and show a way to approach this inequality through sums of Legendre symbols.

This note records that in the setting of complex varieties, the cohomological consequence of Ehresmann's fibration theorem holds without the smooth assumption on the base or the total space.

We characterise finite axiomatisability and intractability of deciding membership for universal Horn classes generated by finite loop-free hypergraphs.

In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.

We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…