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The L(aa)-theory of ordinals is investigated. It is proved that this theory is decidable and that each ordinal is finitely determinate. 0. Introduction. The quantifier "aaA"' with the intended meaning "there is a closed and unbounded system of countable sets X" was introduced by Shelah in  . If we enrich the logic Lau by this quantifier we get the stationary logic Lua(aa). The fundamental paper for the study of stationary logic is  . Stationary logic has a smooth model theory and is adoi:10.2307/1998646 fatcat:75up2yzha5f63iiiaxjjhl5woe