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On Operations and Linear Extensions of Well Partially Ordered Sets

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Abstract

A (partially) ordered set P is well founded if no infinite decreasing sequences occur in P. A well founded poset containing no infinite antichains is called partially well ordered. We investigate some operations preserving that property and linear extensions of partial well orders.

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References

  1. Bollerhoff, U.: On well-quasi-ordering finite sequences, Europ. J. Combin. 10 (1989), 227-230.

    MATH  MathSciNet  Google Scholar 

  2. Erd?s, P. and Rado, R.: Sets having divisor property, solution to problem 4358, Amer. Math. Monthly 59 (1952), 255-257.

    Article  MathSciNet  Google Scholar 

  3. Higman, G.: Ordering by divisibility in abstract algebras, Proc. London Math. Soc. (3) 2 (1952), 326-336.

    MATH  MathSciNet  Google Scholar 

  4. de Jongh, D. H. J. and Parigh, R.: Well-partial orderings and hierachies, Indigationes Math. 39 (1979), 195-207.

    Google Scholar 

  5. Kruskal, J. B.: Well-quasi-ordering, the tree theorem, and Vasonyi’s conjecture, Trans. Amer. Math. Soc. 95 (1960), 210-225.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kruskal, J. B.: The theory of well-quasi-ordering: a frequently discovered concept, J. Combin. Theory (A) (1972), 297-305.

  7. Milner, E. C. and Sauer, N.: On chains and antichains in well founded partially ordered sets, J. London Math. Soc. (2) 24 (1981), 15-33.

    MATH  MathSciNet  Google Scholar 

  8. Neumann, B. H.: On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202-346.

    Article  MATH  MathSciNet  Google Scholar 

  9. Rutkowski, A.: Which countable ordered sets have a dense linear extension? Math. Slovaca 46(5) (1996), 445-455.

    MATH  MathSciNet  Google Scholar 

  10. Schmidt, D.: The relation between the height of a well-founded partial ordering and the order types of its chains and antichains, J. Combin. Theory Ser. B 31 (1981), 183-189.

    Article  MATH  MathSciNet  Google Scholar 

  11. Weiermann, A.: Complexity bounds for some finite forms in Kruskal’s theorem, J. Symbolic Comput. 18 (1994), 463-488.

    Article  MATH  MathSciNet  Google Scholar 

  12. Wolk, E. S.: Partially well ordered sets and partial ordinals, Fund. Math. 60 (1967), 175-186.

    MATH  MathSciNet  Google Scholar 

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Malicki, M., Rutkowski, A. On Operations and Linear Extensions of Well Partially Ordered Sets. Order 21, 7–17 (2004). https://doi.org/10.1007/s11083-004-2738-0

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  • DOI: https://doi.org/10.1007/s11083-004-2738-0

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