Name
Abstract | ||
|---|---|---|
Given a regular uncountable cardinal kappa and a cardinal lambda > kappa of cofinality omega, we show that the restriction of the non-stationary ideal on P-kappa(lambda) to the set of a with cf(sup(a boolean AND kappa)) = omega is not lambda(++) -saturated (and even not 2((lambda<kappa))-saturated in case 2(lambda) = lambda(+)). We actually prove the stronger result that there is Q subset of NG(kappa,lambda)(+) with |Q| - lambda(++) such that A boolean AND B is a non-cofinal subset of P-kappa(lambda) for any two distinct members A, B of Q, where NG(kappa,lambda) denotes the game ideal on P-kappa (lambda). We also remark that for kappa > omega(1), adding lambda(+3) Cohen subsets of omega(1) to L makes NG(kappa,lambda) lambda(+3)-saturated. (C) 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1002/malq.201020055 | MATHEMATICAL LOGIC QUARTERLY |
Keywords | Field | DocType |
P?(?),saturation,MSC (2010) 03E05 | Discrete mathematics,Combinatorics,Countable set,Uncountable set,Cofinality,Mathematics | Journal |
Volume | Issue | ISSN |
58 | 1-2 | 0942-5616 |
Citations | PageRank | References |
2 | 0.43 | 3 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pierre Matet | 1 | 29 | 11.25 |