Automorphism–invariant measures on ℵ0-categorical structures without the independence property

1996 ◽  
Vol 61 (2) ◽  
pp. 640-652
Author(s):  
Douglas E. Ensley
Keyword(s):  
Boolean Algebra ◽  
Invariant Measures ◽  
Measure Zero ◽  
Probability Measures ◽  
Independence Property ◽  
Natural Action ◽  
Zero Sets ◽  
Finitely Additive Probability ◽  
Additive Probability

AbstractWe address the classification of the possible finitely-additive probability measures on the Boolean algebra of definable subsets of M which are invariant under the natural action of Aut(M). This pursuit requires a generalization of Shelah's forking formulas [8] to “essentially measure zero” sets and an application of Myer's “rank diagram” [5] of the Boolean algebra under consideration. The classification is completed for a large class of ℵ0-categorical structures without the independence property including those which are stable.

PROBABILITY MEASURES ON PROJECTIONS IN VON NEUMANN ALGEBRAS

1989 ◽  
Vol 01 (02n03) ◽  
pp. 235-290 ◽  
Author(s):  
SHUICHIRO MAEDA
Keyword(s):  
Probability Measure ◽  
Linear Functional ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
Probability Measures ◽  
Type I ◽  
Von Neumann ◽  
Positive Linear Functional ◽  
Finitely Additive Probability ◽  
Additive Probability

A state ϕ on a von Neumann algebra A is a positive linear functional on A with ϕ(1) = 1, and the restriction of ϕ to the set of projections in A is a finitely additive probability measure. Recently it was proved that if A has no type I 2 summand then every finitely additive probability measure on projections can be extended to a state on A. Here we give precise and complete arguments for proving this result.

scholarly journals Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields

2017 ◽  
Vol 153 (12) ◽  
pp. 2482-2533
Author(s):  
Alexander I. Bufetov ◽  
Yanqi Qiu
Keyword(s):  
Probability Measures ◽  
Symmetric Matrices ◽  
Infinite Matrices ◽  
Locally Compact ◽  
Natural Action ◽  
Ring Of Integers ◽  
Compact Field ◽  
Ergodic Measures

Let$F$be a non-discrete non-Archimedean locally compact field and${\mathcal{O}}_{F}$the ring of integers in$F$. The main results of this paper are the classification of ergodic probability measures on the space$\text{Mat}(\mathbb{N},F)$of infinite matrices with entries in$F$with respect to the natural action of the group$\text{GL}(\infty ,{\mathcal{O}}_{F})\times \text{GL}(\infty ,{\mathcal{O}}_{F})$and the classification, for non-dyadic$F$, of ergodic probability measures on the space$\text{Sym}(\mathbb{N},F)$of infinite symmetric matrices with respect to the natural action of the group$\text{GL}(\infty ,{\mathcal{O}}_{F})$.

Finitely additive probability measures on classical propositional formulas definable by Gödel's t-norm and product t-norm

2011 ◽  
Vol 169 (1) ◽  
pp. 65-90 ◽  
Author(s):  
Aleksandar Perović ◽  
Zoran Ognjanović ◽  
Miodrag Rašković ◽  
Dragan Radojević
Keyword(s):  
Probability Measures ◽  
Finitely Additive Probability ◽  
Additive Probability ◽  
Gödel’S T

scholarly journals Probability logic: A model-theoretic perspective

2020 ◽  
Author(s):  
M Pourmahdian ◽  
R Zoghifard
Keyword(s):  
Characterization Theorem ◽  
Expressive Power ◽  
Probability Logic ◽  
Theoretic Analysis ◽  
Compactness Property ◽  
Probability Models ◽  
Finitely Additive Probability ◽  
Additive Probability ◽  
Basic Probability ◽  
Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

On a classification of theories without the independence property

2013 ◽  
Vol 59 (1-2) ◽  
pp. 119-124 ◽  
Author(s):  
Viktor Verbovskiy
Keyword(s):  
Independence Property

Powers of the ideal of Lebesgue measure zero sets

1991 ◽  
Vol 56 (1) ◽  
pp. 103-107
Author(s):  
Maxim R. Burke
Keyword(s):  
Partial Order ◽  
Lebesgue Measure ◽  
Regular Cardinal ◽  
Measure Zero ◽  
Lebesgue Measure Zero ◽  
Zero Sets ◽  
Covering Lemma ◽  
Inner Model ◽  
The Ideal

AbstractWe investigate the cofinality of the partial order κ of functions from a regular cardinal κ into the ideal of Lebesgue measure zero subsets of R. We show that when add () = κ and the covering lemma holds with respect to an inner model of GCH, then cf (κ) = max{cf(κκ), cf([cf()]κ)}. We also give an example to show that the covering assumption cannot be removed.

Sign in / Sign up

Export Citation Format

Share Document