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Block combinatorics

Author(s): V. Farmaki; S. Negrepontis
Journal: Trans. Amer. Math. Soc. 358 (2006), 2759-2779.
MSC (2000): Primary 03E05; Secondary 05D10, 46B20
Posted: January 27, 2006
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Abstract: In this paper we extend the block combinatorics partition theorems of Hindman and Milliken-Taylor in the setting of the recursive system of the block Schreier families $ (\mathcal{B}^\xi)$, consisting of families defined for every countable ordinal $ \xi$. Results contain (a) a block partition Ramsey theorem for every countable ordinal $ \xi$ (Hindman's Theorem corresponding to $ \xi=1$, and the Milliken-Taylor Theorem to $ \xi$ a finite ordinal), (b) a countable ordinal form of the block Nash-Williams partition theorem, and (c) a countable ordinal block partition theorem for sets closed in the infinite block analogue of Ellentuck's topology.

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Additional Information:

V. Farmaki
Affiliation: Department of Mathematics, Athens University, Athens 157 84, Greece
Email: vfarmaki@math.uoa.gr

S. Negrepontis
Affiliation: Department of Mathematics, Athens University, Athens 157 84, Greece
Email: snegrep@math.uoa.gr

DOI: 10.1090/S0002-9947-06-03864-5
PII: S 0002-9947(06)03864-5
Keywords: Block Ramsey, Nash-Williams combinatorics, Schreier families
Received by editor(s): June 9, 2004
Received by editor(s) in revised form: September 9, 2004.
Posted: January 27, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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