Related papers: Remarks On $\aleph_0$-Injectivity
Reflection, the ability of large language models (LLMs) to evaluate and revise their own reasoning, has been widely used to improve performance on complex reasoning tasks. Yet, most prior works emphasizes designing reflective prompting…
We survey known results and open problems in abelian combinatorics on words. Abelian combinatorics on words is the extension to the commutative setting of the classical theory of combinatorics on words. The extension is based on…
We initiate the study of pseudofiniteness in continuous logic. We introduce a related concept, namely that of pseudocompactness, and investigate the relationship between the two concepts. We establish some basic properties of…
We present a refinement of the Calculus of Inductive Constructions in which one can easily define a notion of relational parametricity. It provides a new way to automate proofs in an interactive theorem prover like Coq.
We prove some injectivity theorems. Our proof depends on the theory of mixed Hodge structures on cohomology groups with compact support. Our injectivity theorems would play crucial roles in the minimal model theory for higher-dimensional…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
In this short article we present some properties regarding the order and the type of an entire function.
We analyze a class of modal logics rendered insensitive to reflexivity by way of a modification to the semantic definition of the modal operator. We explore the extent to which these logics can be characterized, and prove a general…
In this paper we extend our findings in [3] and answer further questions regarding continuity and discontinuity of seminorms on infinite-dimensional vector spaces.
In this paper we classify all $\aleph_0$-categorical and $C$-minimal sets up to elementary equivalence.
In this article, we develop an explicit categorical realization of sheafification based on colimits, products, and subobjects, emphasizing its behavior in algebraic and topological-algebraic settings. We prove that if $\mathcal{C}$ is a…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
The note complements topological aspects of the theory of chiral algebras.
We discuss some aspects of the theory of subelliptic estimates.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
In a general algebraic setting, we state some properties of commutators of reflexive admissible relations.
In this paper, we continue studying the properties of $\gamma$-semi-continuous and $\gamma$-semi-open functions introduced in [5].
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
In earlier work (arXiv:0801.0261), we gave a definition of an abelian category of motivic (constructible) sheaves over a base in characteristic zero using Nori's method. This category has Hodge and etale realizations, and is stable under…