Isomorphisms of scattered automatic linear orders
نویسندگان
چکیده
منابع مشابه
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.
متن کاملTree-automatic scattered linear orders
We study tree-automatic linear orders on regular tree languages. We first show that there is no tree-automatic scattered linear order, and in particular no well-order, on the set of all finite labeled trees. This also follows from results of Gurevich-Shelah [8] and Carayol-Löding [4]. We then show that a regular tree language admits a tree-automatic scattered linear order if and only if all tre...
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We study model-theoretic properties of automatic linear orders, in particular issues of categoricity and suborder complexity. We prove that the growth rate of the domain of a presentation of a linear order dictates the complexity. These results highlight key similarities and differences between automatic structures and other structures of effective mathematics.
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A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific simple trees and a structure is word automatic if it is encodable using only these trees. The question naturally arises whether a given tree automatic structure i...
متن کاملMinimality of Non Σ-scattered Orders
In this paper we will characterize — under appropriate axiomatic assumptions — when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative co...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2014
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2014.03.022