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Definable sets in Stone algebras

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Abstract

We investigate the definable subsets of Stone algebras, introduce the notion of pseudo o-minimality of partially ordered structures, and prove that the completion of the theory of Stone algebras is pseudo o-minimal. We also give the decomposition theorem of Stone algebras.

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References

  1. Baldwin, J., Lachlan, H.: On strongly minimal sets. J. Symb. Logic 36, 79–96 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  2. Lou van den Dries: Tame Topology and o-Minimal Structures. Cambridge University Press, Cambridge (1998)

  3. Pillay, A., Steinhorn, C.: Definable sets in ordered structures III. Trans. AMS 309, 469–476 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  4. Knight, J., Pillay, A., Steinhorn, C.: Definable sets in ordered structures II. Trans. AMS 295, 593–605 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  5. Newelski, L., Wencel, R.: Definable sets in Boolean-ordered o-minimal structures I. J. Symb. Logic 66, 1821–1836 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wencel, R.: Definable sets in Boolean-ordered o-minimal structures II. J. Symb. Logic 68, 35–51 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wencel, R.: Small theories of Boolean-ordered o-minimal structures. J. Symb. Logic 67, 1385–1390 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Toffalori, C.: Lattice ordered o-minimal structures. Notre Dame J. Form. Logic 39, 447–463 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. Schmitt, P.: The model completion of Stone algebras. Ann. Sci. Univ. Clermont 13, 135–155 (1976)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Philosophy, Beijing Normal University, Beijing, 100875, China

    Lei Chen

  2. East Stroudsburg University of Pennsylvania, East Stroudsburg, PA, 18301, USA

    Niandong Shi

  3. Nanyang Technological University of Singapore, Singapore, 637616, Singapore

    Guohua Wu

Authors
  1. Lei Chen
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  2. Niandong Shi
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  3. Guohua Wu
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Corresponding author

Correspondence to Niandong Shi.

Additional information

This work is supported by the National Social Sciences Foundation of China (No. 14BZX078).

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Chen, L., Shi, N. & Wu, G. Definable sets in Stone algebras. Arch. Math. Logic 55, 749–757 (2016). https://doi.org/10.1007/s00153-016-0491-x

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  • DOI: https://doi.org/10.1007/s00153-016-0491-x

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