Related papers: A logical implication between two conjectures on m…
A conjecture of Mumford predicts a complete set of relations between the generators of the cohomology ring of the moduli space of rank 2 semi-stable sheaves with fixed odd degree determinant on a smooth, projective curve of genus at least…
In this paper, we clarify and build connections between various conjectures largely motivated by the works of Jean-Pierre Serre and John Tate. We closely study the Tate conjecture for algebraic cycles as well as their motivic…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
We give an algebraic proof of the criterion for hereditary structural completeness of an intermediate logic, or, equivalently, of the primitiveness of a variety of Heyting algebras.
In 1989, Rota made the following conjecture. Given $n$ bases $B_{1},\dots,B_{n}$ in an $n$-dimensional vector space $V$, one can always find $n$ disjoint bases of $V$, each containing exactly one element from each $B_{i}$ (we call such…
We prove that a triangulated category which is the underlying category of a stable derivator has a filtered enhancement, providing an affirmative answer to a conjecture in [3].
Explanations of Machine Learning (ML) models often address a 'Why?' question. Such explanations can be related with selecting feature-value pairs which are sufficient for the prediction. Recent work has investigated explanations that…
We explore presumptive reasoning in the paraconsistent case. Specifically, we provide semantics for non-trivial reasoning with presumptive arguments with contradictory assumptions or conclusions. We adapt the case models proposed by Verheij…
On a finite structure, the polymorphism invariant relations are exactly the primitively positively definable relations. On infinite structures, these two sets of relations are different in general. Infinitary primitively positively…
This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the…
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general values of positive semidefinite rank we provide a conjecture…
Extension conjecture states that if a simple module over an artin algebra has nonzero first self-extension group then it has nonzero i-th self-extension group for infinitely many positive integers i. It is shown by recollement of…
We provide a framework to study stability notions for two-sided dynamic matching markets in which matching is one-to-one and irreversible. The framework gives center stage to the set of matchings an agent anticipates would ensue should they…
We give a bijective correspondence between the number of nilpotent matrices over a Boolean semiring and the number of directed acyclic graphs on ordered vertices. We then enumerate pairs of maps between two finite sets whose composites are…
We give a simple proof of a crucial lemma that is established in [1, Lemma 2.1] by induction, and plays important roles in that paper and [2].
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$,…
In a recent paper Kent has pointed out that in consistent histories quantum theory it is possible, given initial and final states, to construct two different consistent families of histories, in each of which there is a proposition that can…
We prove a conjecture by D. Zeilberger on the determinant of a certain matrix and relate it to a problem of non-existence of 1-cycles in this note.
We prove that if a standard determinantal scheme is level, then its h-vector is a log-concave pure O-sequence, and conjecture that the converse also holds. Among other cases, we prove the conjecture in codimension two, or when the entries…