An Ehrenfeucht-Fraïssé game approach to collapse results in database theory

  • Authors:

  • Nicole Schweikardt

  • Affiliations:

  • Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany

  • Venue:
  • Information and Computation
  • Year:
  • 2007

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Abstract

Pursuing an Ehrenfeucht-Fraisse game approach to collapse results in database theory, we show that, in principle, every natural generic collapse result may be proved via a translation of winning strategies for the duplicator in an Ehrenfeucht-Fraisse game. Following this approach we can deal with certain infinite databases where previous, highly involved methods fail. We prove the natural generic collapse for Z-embeddable databases over any linearly ordered context structure with arbitrary monadic predicates, and for N-embeddable databases over the context structure , where Groups is the collection of all subgroups of that contain the set of integers and Mon"Q is the collection of all subsets of a particular infinite set Q of natural numbers. This, in particular, implies the collapse for arbitrary databases over and for N-embeddable databases over . That is, first-order logic with , we explicitly construct a winning strategy for the duplicator in the presence of the built-in addition relation +. This, as a side product, also leads to an Ehrenfeucht-Fraisse game proof of the theorem of Ginsburg and Spanier, stating that the spectra of FO(