Indistinguishability and first-order logic

  • Authors:
  • Skip Jordan;Thomas Zeugmann

  • Affiliations:
  • Division of Computer Science, Hokkaido University, Sapporo, Japan;Division of Computer Science, Hokkaido University, Sapporo, Japan

  • Venue:
  • TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
  • Year:
  • 2008

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Abstract

The "richness" of properties that are indistinguishable from first-order properties is investigated. Indistinguishability is a concept of equivalence among properties of combinatorial structures that is appropriate in the context of testability. All formulas in a restricted class of second-order logic are shown to be indistinguishable from first-order formulas. Arbitrarily hard properties, including RE-complete properties, that are indistinguishable from first-order formulas are shown to exist. Implications on the search for a logical characterization of the testable properties are discussed.