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...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Laurent Braud
• Keywords: FSTTCS 2009, Monadic Second-order Formula, Monadic Theory, Pushdown Hierarchy, Theoretical Computer Science