Abstract
We show that for each positive integer n there is a finite list of equivalence relations on [ℚ]n with the property that for every other equivalence relation E on [ℚ]n there is X⊂ℚ of order type equal to the order type of ℚ, such that E↾[X]n is equal to one of the equivalence relations from the list.
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References
Blass, A.: A partition theorem for perfect sets, Proc.Amer.Math.Soc. 82 (1981), 271–277.
Comtet, L.: Advanced Combinatorics, D. Reidel, Dordrecht, 1979.
Devlin, D.: Some partition theorems and ultrafilters on ω, Ph.D. thesis, Dartmouth College, 1979.
Erdös, P. and Rado, R.: A combinatorial theorem, J.London Math.Soc. 25 (1950), 249–255.
Halpern, J. D. and Läuchli, H.: A partition theorem, Trans.Amer.Math.Soc. 124 (1966), 360–367.
Lefmann, H.: Canonical partition behaviour of Cantor spaces, in Irregularities of Partitions (Fertöd, 1986), Algorithms Combin. Study Res. Texts 8, Springer, Berlin, 1989, pp. 93–105.
Milliken, K.: A Ramsey theorem for trees, J.Combin.Theory A 26 (1979), 215–237.
Ramsey, F. P.: On a problem of formal logic, Proc.London Math.Soc. 30 (1930), 264–286.
Todorcevic, S.: Some partitions of three-dimensional cubes, J.Combin.Theory A 68 (1994), 410–437.
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Vuksanovic, V. Canonical Equivalence Relations on ℚn . Order 20, 373–400 (2003). https://doi.org/10.1023/B:ORDE.0000034617.11548.22
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DOI: https://doi.org/10.1023/B:ORDE.0000034617.11548.22