相关论文: Separating the Fan Theorem and Its Weakenings

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

We consider several formalizations in the language of second-order arithmetic of "The formula $\phi$ is a theorem of $\omega$-logic", including some which have been studied in the literature and a new variant defined via a least fixed…

The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…

The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond…

Models of dependent type theories are contextual categories with some additional structure. We prove that if a theory $T$ has enough structure, then the category $T\text{-}\mathbf{Mod}$ of its models carries the structure of a model…

A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type…

We generalise the notion of Gr\"obner fan to ideals in R[[t]][x_1,...,x_n] for certain classes of coefficient rings R and give a constructive proof that the Gr\"obner fan is a rational polyhedral fan. For this we introduce the notion of…

Generalizing the notion of a tight almost disjoint family, we introduce the notions of a {\em tight eventually different} family of functions in Baire space and a {\em tight eventually different set of permutations} of $\omega$. Such sets…

We propose a belief-formation model where agents attempt to discriminate between two theories, and where the asymmetry in strength between confirming and disconfirming evidence tilts beliefs in favor of theories that generate strong (and…

We provides some new equivalent forms of collection principle over some very weak set theories after reviewing the existing ones.

In this short note we give counterexamples to several results related to extension theorems published recently.

Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of…

In this paper, we define quantum toric varieties associated to an arbitrary fan in a finitely generated subgroup of some $\mathbb{R}^d$ generalizing the article arXiv:2002.03876 of Katzarkov, Lupercio, Meersseman and Verjovsky.

In this paper we survey wqo and bqo theory from the reverse mathematics perspective. We consider both elementary results (such as the equivalence of different definitions of the concepts, and basic closure properties) and more advanced…

We prove the Relative Hard Lefschetz theorem and the Relative Hodge-Riemann bilinear relations for combinatorial intersection cohomology sheaves on fans.

We consider a sub-class of the $f$-divergences satisfying a stronger convexity property, which we refer to as strongly convex, or $\kappa$-convex divergences. We derive new and old relationships, based on convexity arguments, between…

The fluctuation theorem establishes general relations between transport coefficients and fluctuations in nonequilibrium systems. Recently there was much interest in quantum fluctuation relations for electric currents. Since charge carriers…

We study the category of KM fans - a "stacky" generalization of the category of fans considered in toric geometry - and its various realization functors to "geometric" categories. The "purest" such realization takes the form of a functor…

We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…

The fluctuation theorem (FT), the first derived consequence of the {\it Chaotic Hypothesis} (CH) of ref. [GC1], can be considered as an extension to arbitrary forcing fields of the fluctuation dissipation theorem (FD) and the corresponding…