Skip to main content
Log in

Ramsey theorems for product of finite sets with submeasures

Combinatorica Aims and scope Submit manuscript

Abstract

We prove parametrized partition theorem on products of finite sets equipped with submeasures, improving the results of Di Prisco, Llopis, and Todorcevic.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Carlos Di Prisco and James Henle: Partitions of products, J. Symbolic Logic 58 (1993), 860–871.

    Article  MathSciNet  MATH  Google Scholar 

  2. Carlos Di Prisco, Jimena Llopis and Stevo Todorcevic: Borel partitions of products of finite sets and the Ackermann function, J. Comb. Theory, Ser. A 93(2) (2001), 333–349.

    Article  MATH  Google Scholar 

  3. Carlos A. Di Prisco, Jimena Llopis and Stevo Todorcevic: Parametrized partitions of products of finite sets, Combinatorica 24(2) (2004), 209–232.

    Article  MathSciNet  MATH  Google Scholar 

  4. David H. Fremlin: Large correlated families of positive random variables, Math. Proc. Cambridge. Philos. Soc. 103 (1988), 147–162.

    Article  MathSciNet  MATH  Google Scholar 

  5. Fred Galvin and Karel Prikry: Borel sets and Ramsey’s theorem, Journal of Symbolic Logic 38 (1973), 193–198.

    Article  MathSciNet  MATH  Google Scholar 

  6. Ronald Graham, Bruce Rothschild and Joel Spencer: Ramsey theory, Wiley, New York, 1990.

    MATH  Google Scholar 

  7. Thomas Jech: Set Theory, Academic Press, San Diego, 1978.

    Google Scholar 

  8. Vladimir Kanovei: Borel Equivalence Relations. Structure and Classification; University Lecture Series 44, American Mathematical Society, Providence, RI, 2008.

    MATH  Google Scholar 

  9. Richard Laver: Products of infinitely many perfect trees, Journal of London Mathematical Society 29 (1984), 385–396.

    Article  MathSciNet  MATH  Google Scholar 

  10. Krzysztof Mazur: F σ-ideals and ω 1 ω 1* gaps in the Boolean algebra P(ω)/I, Fundamenta Mathematicae 138 (1991), 103–111.

    MathSciNet  MATH  Google Scholar 

  11. Andrzej Rosłanowski: n-localization property, Journal of Symbolic Logic 71 (2006), 881–902.

    Article  MathSciNet  MATH  Google Scholar 

  12. Andrzej Rosłanowski and Saharon Shelah: Norms on possibilities I: forcing with trees and creatures; Memoirs of the American Mathematical Society 141, xii + 167 p., 1999. math.LO/9807172.

  13. Jindřich Zapletal: Forcing Idealized, Cambridge Tracts in Mathematics 174, Cambridge University Press, Cambridge, 2008.

    Book  MATH  Google Scholar 

  14. Jindřich Zapletal: Preservation of P-points and definable forcing, submitted to Fundamenta Mathematicae, 2008.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saharon Shelah.

Additional information

Research supported by the United States-Israel Binational Science Foundation (Grant no. 2006108). Publication number 952.

Partially supported by NSF grant DMS 0801114 and Institutional Research Plan No. AV0Z10190503 and grant IAA100190902 of GA AV ČR.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shelah, S., Zapletal, J. Ramsey theorems for product of finite sets with submeasures. Combinatorica 31, 225–244 (2011). https://doi.org/10.1007/s00493-011-2677-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00493-011-2677-5

Mathematics Subject Classification (2000)

Navigation