Related papers: Separating the Fan Theorem and Its Weakenings
IIn the context of a weak formal theory called Basic Intuitionistic Mathematics $\mathsf{BIM}$, we study Brouwer's Fan Theorem and a strong negation of the Fan Theorem, Kleene's Alternative (to the Fan Theorem). We prove that the Fan…
The performance of a fan is usually estimated from hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this work we use kinetic theory to attack this…
We develop a realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving…
Brouwer's fan theorem states that every bar is a uniform bar. We give an overview of the status of this axiom in Bishop's constructive mathematics. In particular, we describe the relationship between the fan theorem, the weak K\"onig lemma,…
The strong continuity principle reads "every pointwise continuous function from a complete separable metric space to a metric space is uniformly continuous near each compact image." We show that this principle is equivalent to the fan…
We study two notions of fan-planarity introduced by (Cheong et al., GD22), called weak and strong fan-planarity, which separate two non-equivalent definitions of fan-planarity in the literature. We prove that not every weakly fan-planar…
The paper is a contribution to intuitionistic reverse mathematics. We introduce a formal system called Basic Intuitionistic Mathematics BIM, and then search for statements that are, over BIM, equivalent to Brouwer's Fan Theorem or to its…
A new class of full fans in an euclidean space - tight fans - is introduced. Such fans are defined using a property of local symmetry in a face of a tiling. Tight fans are related to the theory of parallelotopes in an euclidean space. A…
We show that the following properties are preserved under inverse limits: countable fan-tightness, q+, discrete generation and selective separability. We also present several examples based on inverse limits of countable spaces.
We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Quillen equivalences and most of the usual construction of…
We generalize the finite version of Gowers' Ramsey theorem to multiple tetris-like operations and apply it to show that a group of homeomorphisms that preserve a "typical" linear order of branches of the Lelek fan, a compact connected…
In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then…
We show that a single special separation theorem (namely, a consequence of the geometric form of the Hahn-Banach theorem) can be used to prove Farkas type theorems, existence theorems for numerical quadrature with positive coefficients, and…
In this article, the interplay between Vop\v{e}nka's principle, as well as its weaker counterpart, and presentable $\infty$-categories is studied. Analogous statements, arising after replacing categories with $\infty$-categories in the…
In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…
We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic…
In this paper we study admissible extensions of several theories T of reverse mathematics. The idea is that in such an extension the structure M = (N,S,\in) of the natural numbers N and collection of sets of natural numbers S has to obey…
The stable Ramsey's theorem for pairs has been the subject of numerous investigations in mathematical logic. We introduce a weaker form of it by restricting from the class of all stable colorings to subclasses of it that are non-null in a…
There are several extensions of the classical Banach Fixed Point Theorem in technical literature. A branch of generalizations replaces usual contractivity by weaker but still effective assumptions. Our note follows this stream, presenting…
We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.