11 citations · 27 across the 16 of their papers we have counts for
13 papers · 1 filter
Mathias and Silver forcing parametrized by density
Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle
We define and investigate versions of Silver and Mathias forcing with respect to lower and upper density. We focus on properness, Axiom A, chain conditions, preservation of cardina…
On the Representation and Construction of Equitable Social Welfare Orders
Ram Sewak Dubey, Giorgio Laguzzi, Francesco Ruscitti
This paper examines the representation and explicit description of social welfare orders on infinite utility streams. It is assumed that the social welfare orders under investigati…
Laver Trees in the Generalized Baire Space
Yurii Khomskii, Marlene Koelbing, Giorgio Laguzzi +1
We prove that any suitable generalization of Laver forcing to the space , for uncountable regular , necessarily adds a Cohen -real. We also study a dichotomy and an ide…
Some considerations on Amoeba forcing notions
Giorgio Laguzzi
In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision…
Uncountable trees and Cohen -reals
Giorgio Laguzzi
We investigate some versions of amoeba for tree-forcings in the generalized Cantor and Baire spaces. This answers [10, Question 3.20] and generalizes a line of research that in the…
Generalized Silver and Miller measurability
Giorgio Laguzzi
We present some results about the burgeoning research area concerning set theory of the kappa-reals. We focus on some notions of measurability coming from generalizations of Silver…
A null ideal for inaccessibles
Sy David Friedman, Giorgio Laguzzi
In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of the generalised Cantor space and study its associated ideal…
On the sepration of regularity properties of the reals
Giorgio Laguzzi
We present a model where ω_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…
The non-democratic side of regular sets
Giorgio Laguzzi
We analyse the role and the possible interpretations of regular sets studied in descriptive set theory and forcing theory from the point of view of social choice theory and we prov…
More on trees and Cohen reals
Giorgio Laguzzi, Brendan Stuber-Rousselle
In this paper we analyse some questions concerning trees on , both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a…
On splitting trees
Giorgio Laguzzi, Heike Mildenberger, Brendan Stuber-Rousselle
We investigate two variants of splitting tree forcing, their ideals and regularity properties. We prove connections with other well-known notions, such as Lebesgue measurablility,…
Paretian social welfare relations and Baire property
Giorgio Laguzzi, Ram Sewak Dubey
We study the topological and set-theoretical nature of Paretian social welfare relations in a setting with infinite time horizon. Specifically, we answer questions posed in \citet{…
Social welfare relations and irregular sets
Ram Sewak Dubey, Giorgio Laguzzi
Total social welfare relations satisfying Pareto and equity principles on infinite utility streams has revealed a non-constructive nature. In this paper we study more deeply the ne…