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FSTTCS

2009

Springer

2009

Springer

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...

Related Content

Added |
26 May 2010 |

Updated |
26 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
FSTTCS |

Authors |
Laurent Braud |

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