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Uniqueness of the Core for Chain-Complete Ordered Sets

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Abstract

It is proved that the C-core of a chain-complete ordered set is unique up to isomorphism if it exists. We also give an example that shows that the (U C∪L C)-core of an ordered set need not be unique. This is related to a question, which asks if the P-core is unique if it exists.

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References

  1. Abian, S. and Brown, A. B. (1961) A theorem on partially ordered sets with applications to fixed point theorems, Canad. J. Math. 13, 78–82.

    Google Scholar 

  2. Cousot, P. and Cousot, R. (1979) Constructive versions of Tarski' fixed point theorems, Pacific J. Math. 82, 43–57.

    Google Scholar 

  3. Duffus, D., Poguntke, W. and Rival, I. (1980) Retracts and the fixed point problem for finite partially ordered sets, Canad. Math. Bull. 23, 231–236.

    Google Scholar 

  4. Duffus, D. and Rival, I. (1976) Crowns in dismantlable partially ordered sets, Coll. Math. Soc. Janos Bolyai 18, 271–292.

    Google Scholar 

  5. Farley, J. D. (1993) The uniqueness of the core, Order 10, 129–131.

    Google Scholar 

  6. Farley, J. D. (1997) Perfect sequences of chain-complete posets, Discrete Math. 167/168, 271–296.

    Google Scholar 

  7. Li, B. (1993) The core of a chain complete poset with no one-way infinite fence and no tower, Order 10, 349–361.

    Google Scholar 

  8. Li, B. and Milner, E. C. (1992) The PT order and the fixed point property, Order 9, 321–331.

    Google Scholar 

  9. Li, B. and Milner, E. C. (1993) A chain complete poset with no infinite antichain has a finite core, Order 10, 55–63.

    Google Scholar 

  10. Li, B. and Milner, E. C. (1995) From finite posets to chain complete posets having no infinite antichain, Order 12, 159–171.

    Google Scholar 

  11. Pelczar, A. (1961) On the invariant points of a transformation, Ann. Polon. Math. XI, 199–202.

    Google Scholar 

  12. Roddy, M. (1994) Cores and retracts, Order 11, 1–9.

    Google Scholar 

  13. Schröder, B. (1999) Algorithms for the fixed point property, Theoret. Comput. Sci. 217, 301–358.

    Google Scholar 

  14. Walker, J. W. (1984) Isotone relations and the fixed point property for posets, Discrete Math. 48, 275–288.

    Google Scholar 

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  1. Program of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, U.S.A.

    Bernd S. W. Schröder

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  1. Bernd S. W. Schröder
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Schröder, B.S.W. Uniqueness of the Core for Chain-Complete Ordered Sets. Order 17, 207–214 (2000). https://doi.org/10.1023/A:1026536923600

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