Related papers: Tracking chains revisited

We prove, in ZFC, that there is an infinite strictly descending chain of classes of theories in Keisler's order. Thus Keisler's order is infinite and not a well order. Moreover, this chain occurs within the simple unstable theories,…

Carlsson's construction is a simplicial group whose geometric realization is the loop space of the 1-stunted reduced Borel construction. Our main results are: i) Given a pointed simplicial set acted upon by the discrete cyclic group C_2 of…

All Lipschitz dynamics with the weak infinitesimal contraction (WIC) property can be expressed as a Lipschitz nonlinear system in proportional negative feedback -- this statement, a ``structure theorem,'' is true in the $p=1$ and $p=\infty$…

We provide a statistical analysis of regularization-based continual learning on a sequence of linear regression tasks, with emphasis on how different regularization terms affect the model performance. We first derive the convergence rate…

Structure of certain simple $\mathcal{W}$-algebras assocated with the Deligne exceptional Lie algebras and non-admissible levels are described as the {\it simple current extensions} of certain vertex operator algebras. As an application,…

We formalize the concept of subtime -- a reversible mode of information interchange within entangled systems -- and show how classical time emerges as an asymptotic limit through decoherence. Building on the photon clock model, in which a…

This paper introduces a partial order on the maximal chains of any finite bounded poset $P$ which has a CL-labeling $\lambda$. We call this the maximal chain descent order induced by $\lambda$, denoted $P_{\lambda}(2)$. As a first example,…

An addition chain for $n$ is defined to be a sequence $(a_0,a_1,\ldots,a_r)$ such that $a_0=1$, $a_r=n$, and, for any $1\le k\le r$, there exist $0\le i, j<k$ such that $a_k = a_i + a_j$; the number $r$ is called the length of the addition…

We define and study the canonical complex of a finite semidistributive lattice $L$. It is the simplicial complex on the join or meet irreducible elements of $L$ which encodes each interval of $L$ by recording the canonical join…

Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…

Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…

Causal discovery is the challenging task of inferring causal structure from data. Motivated by Pearl's Causal Hierarchy (PCH), which tells us that passive observations alone are not enough to distinguish correlation from causation, there…

This paper is an investigation of the relationship between G\"odel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of Spector's that the relation $\{(A,B) \in \mathbb{R}^2 :…

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of…

$W$-graphs, representing the multiplication action of the standard basis on the canonical basis in the Iwahori-Hecke algebra are introduced by Kazhdan and Lusztig. Marberg defined a generalized $W$-graph, the Gelfand W-graph, corresponding…

Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…

Generalised indiscernibles highlight a strong link between model theory and structural Ramsey theory. In this paper, we use generalised indiscernibles as tools to prove results in both these areas. More precisely, we first show that a…

This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

Let $R$ be a not necessarily commutative ring with $1.$ In the present paper we first introduce a notion of quasi-orderings, which axiomatically subsumes all the orderings and valuations on $R$. We proceed by uniformly defining a coarsening…