相关论文: Algebraic characterizations of measure algebras
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
In this paper we discuss the existence of a control measure for a family of measures on a Boolean algebra. We obtain a necessary and sufficient condition and several related results, including a new criterion for weak compactness for…
The paper investigates possible generalisations of Maharam's theorem to a classification of Boolean algebras that support a finitely additive measure. We prove that Boolean algebras that support a finitely additive non-atomic uniformly…
By the additive property, we mean a condition under which $L^p$ spaces over finitely additive measures are complete. Basile and Rao gives a necessary and sufficient condition that a finite sum of finitely additive measures has the additive…
A Boolean $\sigma$-algebra $B$ is a measure algebra if and only if it is weakly distributive and uniformly concentrated.
We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…
We give a necessary and sufficient condition for an atomless Boolean algebra to be countably generated, and use it to give new proofs of some some know facts due to Gaifman-Hales and Solovay and also due to Jech, Kunen and Magidor. We also…
A Boolean algebra carries a strictly positive exhaustive submeasure if and only if it has a sequential topology that is uniformly Frechet.
We give a unified treatment of the model theory of various enrichments of infinite atomic Boolean algebras, with special attention to quantifier-eliminations, complete axiomatizations and decidability. A classical example is the enrichment…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
We investigate reflection-type problems on the class SPM, of Boolean algebras carrying strictly positive finitely additive measures. We show, in particular, that in the constructible universe there is a Boolean algebra $\mathfrak A$ which…
We study the interplay between properties of measures on a Boolean algebra A and forcing names for ultrafilters on A. We show that several well known measure theoretic properties of Boolean algebras (such as supporting a strictly positive…
A necessary and sufficient condition for an element of an algebra (in the sense of Universal Algebra) to be in the dominion of a subalgebra is given, in terms of transferable sets. This criterion is then used to formulate a more wieldy…
It is shown that universal algebras that are injective in their equational classes are characterized by internal property that can be called completeness. We define universal algebra $A$ as complete (closed to simple extensions) if for each…
We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.
We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily…
We study measures, finitely additive measures, regular measures, and $\sigma$-additive measures that can attain even infinite values on the quantum logic of a Hilbert space. We show when particular classes of non-negative measures can be…
We parameterize countable locally standard measure algebras by pairs of a Steinitz number and a real number greater or equal to 1. This is an analog of the theorems of J.Dixmier and A.A.Baranov.
We characterize the situation of having many normal measures on a measurable cardinal. We show the plausibility of having many normal measures on each compact cardinal.
We introduce the notion of amenability for affine algebras. We characterize amenability by Folner-sequences, paradoxicality and the existence of finitely invariant dimension-measures. Then we extend the results of Rowen on ranks, from…