Gurevich, Yuri; Shelah, Saharon On finite rigid structures. (English) Zbl 0860.03029 J. Symb. Log. 61, No. 2, 549-562 (1996). 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 \(L^\omega_{\infty \omega}\). Reviewer: J.Flum (Freiburg i.Br.) Cited in 1 ReviewCited in 14 Documents MSC: 03C13 Model theory of finite structures 03C75 Other infinitary logic 03C50 Models with special properties (saturated, rigid, etc.) Keywords:infinitary logic; finite structures; fixed-point logic; rigid structures PDFBibTeX XMLCite \textit{Y. Gurevich} and \textit{S. Shelah}, J. Symb. Log. 61, No. 2, 549--562 (1996; Zbl 0860.03029) 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.