IRCS Technical Reports Series

Document Type

Technical Report

Date of this Version

February 1996

Comments

University of Pennsylvania Institute for Research in Cognitive Science Technical Report No. IRCS-96-02.

Abstract

This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number of variables and that there exist k-universal graphs with no k-extendible induced subgraphs.

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Date Posted: 07 August 2006