The Model-Theoretic Complexity of Automatic Linear Orders
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Beschreibung
Automatic structures are—possibly infinite—structures which are finitely presentable by means of finite automata on strings or trees. Largely motivated by the fact that their first-order theories are uniformly decidable, automatic structures gained a lot of attention in the "logic in computer science" community during the last fifteen years. This thesis studies the model-theoretic complexity of automatic linear orders in terms of two complexity measures: the finite-condensation rank and the Ramsey degree. The former is an ordinal which indicates how far a linear order is away from being dense. The corresponding main results establish optimal upper bounds on this rank with respect to several notions of automaticity. The Ramsey degree measures the model-theoretic complexity of well-orders by means of the partition relations studied in combinatorial set theory. This concept is investigated in a purely set-theoretic setting as well as in the context of automatic structures.
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Bestellungen direkt an den Auslieferer richten!
Auslieferung erfolgt durch:
Brockhaus / Commission, Kornwestheim
E-Mail: readbox@brocom.de
Fax: 07154 1327 13
Autor*in
Martin Huschenbett
Themen in »The Model-Theoretic Complexity of Automatic Linear Orders«
Ramsey theory finite-condensation rank partition relations