Generalizations and Galois-Tukey Connections

  • Christopher S. Hardin
  • Alan D. Taylor
Part of the Developments in Mathematics book series (DEVM, volume 33)


It is possible to see the hat problem on the parity relation as actually being a two-agent hat problem, though we must consider a more general type of hat problem; in doing so, we uncover a close relationship with so-called Galois-Tukey connections. In this final chapter, we explore the relationships between results extending those in Chapter 4 and these Galois-Tukey connections.


Infinite Chain Visibility Graph Actual Color Cardinal Invariant Acceptability Relation 
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  1. [Bar10]
    Bartoszyński, T.: Invariants of measure and category. In: Foreman, M., Kanamori, A. (eds.) Handbook of Set Theory, vol. 1, pp. 491–555. Springer, Dordrecht (2010)CrossRefGoogle Scholar
  2. [Bla10]
    Blass, A.: Combinatorial cardinal characteristics of the continuum. In: Foreman, M., Kanamori, A. (eds.) Handbook of Set Theory, vol. 1, pp. 395–489. Springer, Dordrecht (2010)CrossRefGoogle Scholar
  3. [Mild97]
    Mildenberger, H.: Non-constructive Galois-Tukey connections. J. Symb. Logic 62(4), 1179–1186 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  4. [V93]
    Vojtáš, P.: Generalized Galois-Tukey connections between explicit relations on classical objects of real analysis. In: Judah, H. (ed.) Set Theory of the Reals, Israel Mathematical Conference Proceedings, vol. 6, pp. 619–643. American Mathematical Society, Providence (1993)Google Scholar
  5. [Yip94]
    Yiparaki, O.: On some tree partitions. PhD thesis, University of Michigan (1994)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Christopher S. Hardin
    • 1
  • Alan D. Taylor
    • 2
  1. 1.New YorkUSA
  2. 2.Department of MathematicsUnion CollegeSchenectadyUSA

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