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

Publisher: Cambridge University Press

E-ISSN: 1943-5886|61|2|640-652

ISSN: 0022-4812

Source: The Journal of Symbolic Logic, Vol.61, Iss.2, 1996-06, pp. : 640-652

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Abstract

We 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.