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Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
In this paper we give a sufficient condition of the existence of ${\rm \mathbb{W}}^{t}$-approximation presentations. We also introduce property (W$^{k}$). As an application of the existence of ${\rm \mathbb{W}}^{t}$-approximation…
We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
I comment critically on the use and misuse of the theory of vacuum, pseudoparticles and pseudotensors. The mathematical and phenomenological arguments against the Higgs mechanism and the inflationary scenario are presented. I conclude with…
Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability…
Our main result is the equivalence of two notions of reducibility between structures. One is a syntactical notion which is an effective version of interpretability as in model theory, and the other one is a computational notion which is a…
We prove an iteration theorem which guarantees for a wide class of nice iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a…
We study the question of constructive approximation of the harmonic measure $\omega_x^\Omega$ of a connected bounded domain $\Omega$ with respect to a point $x\in\Omega$. In particular, using a new notion of computable harmonic…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
All spaces are assumed to be separable and metrizable. Our main result is that the statement "For every space $X$, every closed subset of $X$ has the perfect set property if and only if every analytic subset of $X$ has the perfect set…
The hidden-variables premise is shown to be equivalent to the existence of generic filters for algebras of commuting propositions and for certain more general propositional systems. The significance of this equivalence is interpreted in…
For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the…
A Kaufmann model is an $\omega_1$-like, recursively saturated, rather classless model of $\mathrm{PA}$ or $\mathrm{ZF}$. Such models were constructed by Kaufmann under the combinatorial principle $\diamondsuit_{\omega_1}$ and Shelah showed…
In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.
We prove a model theorem for factor maps between ergodic, infinite measure-preserving systems.
In this note we provide a simple proof of some properties enjoyed by convex functions having the engulfing property. In particular, making use only of results peculiar to convex analysis, we prove that differentiability and strict convexity…