Journal of Symbolic Logic

First-order and counting theories of ω-automatic structures

Dietrich Kuske and Markus Lohrey

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The logic ℒ(𝒬u) extends first-order logic by a generalized form of counting quantifiers (“the number of elements satisfying … belongs to the set C”). This logic is investigated for structures with an injectively ω-automatic presentation. If first-order logic is extended by an infinity-quantifier, the resulting theory of any such structure is known to be decidable [6]. It is shown that, as in the case of automatic structures [21], also modulo-counting quantifiers as well as infinite cardinality quantifiers (“there are κ many elements satisfying …”) lead to decidable theories. For a structure of bounded degree with injective ω-automatic presentation, the fragment of ℒ(𝒬u) that contains only effective quantifiers is shown to be decidable and an elementary algorithm for this decision is presented. Both assumptions (ω-automaticity and bounded degree) are necessary for this result to hold.

Article information

Source
J. Symbolic Logic Volume 73, Issue 1 (2008), 129-150.

Dates
First available in Project Euclid: 16 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1208358745

Digital Object Identifier
doi:10.2178/jsl/1208358745

Mathematical Reviews number (MathSciNet)
MR2387935

Zentralblatt MATH identifier
1141.03015

Citation

Kuske, Dietrich; Lohrey, Markus. First-order and counting theories of ω-automatic structures. J. Symbolic Logic 73 (2008), no. 1, 129--150. doi:10.2178/jsl/1208358745. https://projecteuclid.org/euclid.jsl/1208358745.


Export citation