Isomorphisms of scattered automatic linear orders

We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic linear orders, we determine the exact level of undecidability in the arithmetical hierarchy

The isomorphism problem for tree-automatic ordinals with addition

This paper studies tree-automatic ordinals (or equivalently, well-founded linearly ordered sets) together with the ordinal addition operation +. Informally, these are ordinals such that their elements are coded by finite trees for which the linear order relation of the ordinal and the ordinal addition operation can be determined by tree automata. We describe an algorithm that, given two tree-automatic ordinals with the ordinal addition operation, decides if the ordinals are isomorphic

The model-theoretic complexity of automatic linear orders

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.Auch im Buchhandel erhältlich: The model-theoretic complexity of automatic linear orders / Martin Huschenbett Ilmenau : Univ.-Verl. Ilmenau, 2016. - xiii, 228 Seiten ISBN 978-3-86360-127-0 Preis (Druckausgabe): 16,50