The two-variable fragment with counting and equivalence

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    We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NExpTime-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.
    Original languageEnglish
    Pages (from-to)474-515
    Number of pages41
    JournalMathematical Logic Quarterly
    Issue number6
    Publication statusPublished - 25 Nov 2015


    • Two-variable fragment
    • Counting quantifier
    • Equivalence relation


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