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Well-Quasi-Ordering Hereditarily Finite Sets

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Book cover Language and Automata Theory and Applications (LATA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6638))

Abstract

Recently, strong immersion was shown to be a well-quasi-order on the class of all tournaments. Hereditarily finite sets can be viewed as digraphs, which are also acyclic and extensional. Although strong immersion between extensional acyclic digraphs is not a well-quasi-order, we introduce two conditions that guarantee this property. We prove that the class of extensional acyclic digraphs corresponding to slim sets (i.e. sets in which every memebership is necessary) of bounded skewness (i.e. sets whose ∈-distance between their elements is bounded) is well-quasi-ordered by strong immersion.

Our results hold for sets of bounded cardinality and it remains open whether they hold in general.

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References

  1. Abdulla, P., Delzanno, G., Van Begin, L.: A classification of the expressive power of well-structured transition systems. Information and Computation (in Press)

    Google Scholar 

  2. Ackermann, W.: Die Widerspruchfreiheit der allgemeinen Mengenlehre. Mathematische Annalen 114, 305–315 (1937)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bang-Jensen, J., Gutin, G.: Digraphs Theory, Algorithms and Applications, 1st edn. Springer, Berlin (2000)

    MATH  Google Scholar 

  4. Bollobás, B.: Combinatorics. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  5. Chudnovsky, M., Seymour, P.D.: A well-quasi-order for tournaments. J. Comb. Theory, Ser. B 101(1), 47–53 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere? Theoretical Computer Science 256(1-2), 63–92 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  9. Levy, A.: Basic Set Theory. Springer, Berlin (1979)

    Book  MATH  Google Scholar 

  10. Nash-Williams, C.S.J.A.: On well-quasi-ordering trees. In: Theory of Graphs and Its Applications (Proc. Symp. Smolenice, 1963), pp. 83–84. Publ. House Czechoslovak Acad. Sci. (1964)

    Google Scholar 

  11. Omodeo, E.G., Policriti, A.: The Bernays-Schönfinkel-Ramsey class for set theory: semidecidability. J. Symb. Log. 75(2), 459–480 (2010)

    Article  MATH  Google Scholar 

  12. Parlamento, F., Policriti, A., Rao, K.: Witnessing Differences Without Redundancies. Proc. of the American Mathematical Society 125(2), 587–594 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  13. Robertson, N., Seymour, P.: Graph minors. XX. Wagner’s conjecture. J. Combin. Theory, Ser. B 92, 325–357 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Robertson, N., Seymour, P.: Graph minors. XXIII. Nash–Williams’s immersion conjecture. J. Combin. Theory, Ser. B 100, 181–205 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze, 206, 33100, Udine, Italy

    Alberto Policriti & Alexandru I. Tomescu

  2. Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, 010014, Bucharest, Romania

    Alexandru I. Tomescu

Authors
  1. Alberto Policriti
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  2. Alexandru I. Tomescu
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Avinguda Catalunya, 35, 43002, Tarragona, Spain

    Adrian-Horia Dediu  & Carlos Martín-Vide  & 

  2. Department of Informatics, Kyushu University, 744 Motooka, 819–0395, Fukuoka, Japan

    Shunsuke Inenaga

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Policriti, A., Tomescu, A.I. (2011). Well-Quasi-Ordering Hereditarily Finite Sets. In: Dediu, AH., Inenaga, S., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2011. Lecture Notes in Computer Science, vol 6638. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21254-3_35

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  • DOI: https://doi.org/10.1007/978-3-642-21254-3_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21253-6

  • Online ISBN: 978-3-642-21254-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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