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Partitioning  -large sets: Some lower bounds |
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| Authors: | Teresa Bigorajska Henryk Kotlarski |
| Institution: | Faculty of Mathematics, Cardinal Stefan Wyszynski University, ul. Dewajtis 5, 01--815 Warszawa, Poland ; Faculty of Mathematics, Cardinal Stefan Wyszynski University, ul. Dewajtis 5, 01--815 Warszawa, Poland -- and -- Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, P.O. Box 137, 00--950 Warszawa, Poland |
| Abstract: | Let  denote the property: if  is an  -large set of natural numbers and ![$ A]^r$](http://www.ams.org/tran/2006-358-11/S0002-9947-06-03883-9/gif-abstract0/img4.gif){kind=small} is partitioned into  parts, then there exists a  -large subset of  which is homogeneous for this partition. Here the notion of largeness is in the sense of the so-called Hardy hierarchy. We give a lower bound for  in terms of  for some specific  . |
| Keywords: | Ramsey theorem Hardy hierarchy $\alpha$--large sets |
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