×

On finite rigid structures. (English) Zbl 0860.03029

The authors refute a conjecture of A. Dawar stating that if \(K\) is a first-order definable class of rigid finite structures, then there is a formula of fixed-point logic that defines a linear order on every member \(K\). By a probabilistic construction of finite rigid structures they obtain such a \(K\), where not even a formula of \(L^\omega_{\infty \omega}\) with counting quantifiers defines a linear order. In the meantime the construction has been used to show that there are queries implicitly first-order definable that are not definable in \(L^\omega_{\infty \omega}\).

MSC:

03C13 Model theory of finite structures
03C75 Other infinitary logic
03C50 Models with special properties (saturated, rigid, etc.)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1007/978-1-4612-4478-3_5 · doi:10.1007/978-1-4612-4478-3_5
[2] Proceedings of the 7th IEEE Annual Symposium on Logic in Computer Science pp 64– (1992)
[3] Current trends in theoretical computer science pp 1– (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.