Covering of ordinals

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Covering of ordinals
The paper focuses on the structure of fundamental sequences of ordinals smaller than ε0. A first result is the construction of a monadic second-order formula identifying a given structure, whereas such a formula cannot exist for ordinals themselves. The structures are precisely classified in the pushdown hierarchy. Ordinals are also located in the hierarchy, and a direct presentation is given. A recurrent question in computational model theory is the problem of model checking, i.e. the way to decide whether a given formula holds in a structure or not. When studying infinite structures, first-order logic only brings local properties whereas second-order logic is most of the time undecidable, so monadic second-order logic or one of its variants is often a balanced option. In the field of countable ordinals, results of B¨uchi [3] and Shelah [15] both brought decidability of the monadic theory via different ways. This positive outcome is tainted with the following property : the mon...
Laurent Braud
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Authors Laurent Braud
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