1,720,980 research outputs found
On the separation of regularity properties of the reals
Full text linkWe present a model where omega (1) is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman (see [7]), regarding the separation of different notions of regularity properties of the real line
Full-splitting Miller trees and infinitely often equal reals
No full textWe investigate two closely related partial orders of trees on omega(omega) : the full-splitting Miller trees and the infinitely often equal trees, as well as their corresponding sigma-ideals. The former notion was considered by Newelski and Roslanowski while the latter involves a correction of a result of Spinas. We consider some Marczewski-style regularity properties based on these trees, which turn out to be closely related to the property of Baire, and look at the dichotomies of Newelski- Roslanowski and Spinas for higher projective pointclasses. We also provide some insight concerning a question of Fremlin whether one can add an infinitely often equal real without adding a Cohen real, which was recently solved by Zapletal. (C) 2017 Elsevier B.V. All rights reserved
A null ideal for inaccessibles
No full textIn this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of , inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah (On CON(Dominatinglambdacov(meagre)), arXiv:0904.0817, Problem 0.5) and concerns the definition of a forcing which is -bounding, -closed and -cc, for inaccessible. Cohen and Shelah (Generalizing random real forcing for inaccessible cardinals, arXiv:1603.08362) provide a proof for (Shelah, On CON(Dominatinglambdacov(meagre)), arXiv:0904.0817, Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper (Khomskii et al. in Math L Q 62(4-5):439-456, 2016)
Equitable preference relations on infinite utility streams
No full textWe propose generalized versions of strong equity and Pigou-Dalton transfer principle. We study the existence and the real-valued representation of social welfare relations satisfying these two generalized equity principles. Our results characterize the restrictions on one period utility domains for the equitable social welfare relations (i) to exist; and (ii) to admit real-valued representations. (C) 2021 Elsevier B.V. All rights reserved
More on trees and Cohen reals
No full textIn this paper we analyse some questions concerning trees on kappa, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in [6, Question 5.2] about the diagram for regularity properties
On the representation and construction of equitable social welfare orders
No full textThis paper examines the representation and explicit description of social welfare orders on infinite utility streams. It is assumed that the social welfare orders under investigation satisfy upper asymptotic Pareto and anonymity axioms. We prove that there exists no real-valued representation of such social welfare orders. In addition, we establish that the existence of a social welfare order satisfying the anonymity and upper asymptotic Pareto axioms implies the existence of a non-Ramsey set, which is a non-constructive object. Thus, we conclude that the social welfare orders under study do not admit explicit description. (C) 2020 Elsevier B.V. All rights reserved
Decision-making under risk: when is utility-maximization equivalent to risk-minimization?
No full textMotivated by the analysis of a general optimal portfolio selection problem, which encompasses as special cases an optimal consumption and an optimal debt-arrangement problem, we are concerned with the questions of how a personality trait like risk-perception can be formalized and whether the two objectives of utility-maximization and risk-minimization can be both achieved simultaneously. We address these questions by developing an axiomatic foundation of preferences for which utility-maximization is equivalent to minimizing a utility-based shortfall risk measure. Our axiomatization hinges on a novel axiom in decision theory, namely the risk-perception axiom
Generalized Silver and Miller measurability
No full text1 We present some results about the burgeoning research area concern-ing set theory of the “κ-reals”. We focus on some notions of measurability coming from generalizations of Silver and Miller trees. We present analo-gies and mostly differences from the classical setting. 1 Introduction and basic definitions The study of the generalized version of the Baire space κκ and Cantor space 2κ, for κ uncountable regular cardinal, is a burgeoning research area, which intersects both the generalized descriptive set theory and the set theory of the “κ-reals”, where we refer to the elements of κκ and 2κ as κ-reals
Tert-butyl amine borane complex: An unusual application of a reducing agent on model molecules of cellulose based materials
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