Let B be a complete Boolean algebra. We show that if λ is an infinite cardinal and B is weakly (λ, ω)-distributive, then B is (λ, 2)-distributive. Using a similar argument, we show that if κ is a weakly compact cardinal such that B is weakly (2, κ)distributive and B is (α, 2)-distributive for each α < κ, then B is (κ, 2)-distributive.

Abstract This article describes a novel pattern of interpretations associated with universal determiners like ‘each’ and ‘every’. It is demonstrated that these canonically distributive quantifiers can give rise to surprising collective readings when they quantify into sub-clausal constituents, especially other Determiner Phrases. For instance, ‘two cards from each player’ be understood pick out...

This paper discusses the structure that incorporates information from discourse to derive distributivity. Following a proposal by López (2009) to account for the interpretation shown in the canonical focus structure using the notion “contrast”, I suggest that the feature “contrast” assigned to the edge of CP results in distributivity to the extent that distributivity occurs if and only if predi...

This is the first in a pair of papers that aim to provide a comprehensive analysis of the semantic phenomenon of distributivity in natural language. This paper investigates and formalizes different sources of covert distributivity. Apart from lexical distributivity effects, which are modeled by meaning postulates, phrasal distributivity is captured via two covert operators: (i) a D operator dis...

– describe the patterns of interpretation and outline the emerging typology involved in relating: (i) various kinds of distributive quantifiers and (ii) various kinds of distributivity-dependent items – formally capture these patterns and typology in a logical system that involves: (i) fine-grained, structured contexts of evaluation that distributivity-dependent items are sensitive to (ii) a fa...