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First order logic, fixed point logic and linear order

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Computer Science Logic (CSL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1092))

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Abstract

The Ordered conjecture of Kolaitis and Vardi asks whether fixed-point logic differs from first-order logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures of McColm, which arose from the study of inductive definability and infinitary logic on proficient classes of finite structures (those admitting an unbounded induction). In particular, for a class of finite structures, we introduce a compactness notion which yields a new proof of a ramified version of McColm's second conjecture. Furthermore, we show a connection between a model-theoretic preservation property and the Ordered Conjecture, allowing us to prove it for classes of strings (colored orderings). We also elaborate on complexity-theoretic implications of this line of research.

Research supported by EPSRC grant GR/H 81108

Partially supported by NSF grant CCR-9403447, and the John C. Whitehead faculty research fund at Haverford College

Supported in part by NSF CCR-9403447.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Univ. of Wales, SA2 8PP, Swansea, Swansea, UK

    Anuj Dawar

  2. Dept. of Computer Science, Haverford College, 19041, Haverford, PA, USA

    Steven Lindell

  3. Dept. of Philosophy, Univ. of Pennsylvania, 19104, Philadelphia, PA, USA

    Scott Weinstein

Authors
  1. Anuj Dawar
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  2. Steven Lindell
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  3. Scott Weinstein
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Editor information

Hans Kleine Büning

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© 1996 Springer-Verlag Berlin Heidelberg

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Dawar, A., Lindell, S., Weinstein, S. (1996). First order logic, fixed point logic and linear order. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_37

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  • DOI: https://doi.org/10.1007/3-540-61377-3_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61377-0

  • Online ISBN: 978-3-540-68507-4

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