Abstract
We study the relationship between the infinitary logic L ω∞ω with finitely many variables and implicit definability in effective fragments of L ω∞ω on finite structures. We show that fixpoint logic has strictly less expressive power than first-order implicit definability. We also establish that the separation of fixpoint logic from a certain restriction of first-order implicit definability to L ω∞ω is equivalent to the separation of PTIME from UP ∩ co-UP. Finally, we delineate the relationship between partial fixpoint logic and implicit definability in partial fixpoint logic on finite structures.
Research supported by EPSRC grant GR/H 81108.
Research of this author partially supported by NSF Grants INT-9024681 and CCR-9307758.
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Dawar, A., Hella, L., Kolaitis, P.G. (1995). Implicit definability and infinitary logic in finite model theory. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_110
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DOI: https://doi.org/10.1007/3-540-60084-1_110
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