Notes on \(P_{\kappa}\lambda\) and \([\lambda]^{\kappa}\) (Q1092899)

This paper consists of notes on some combinatorial properties. {\S} 1 deals with \(\lambda\)-ineffability and the partition property of \(P_{\kappa}\lambda\) with \(\lambda\) ineffable. In {\S} 2 we combine the flipping property and a filter investigated by Di Prisco and Marek to characterize huge cardinals. We work in ZFC and the notations are standard. \(P_{\kappa}\lambda =\{x\subset \lambda:| x| <\kappa \}\), \([\lambda]^{\kappa}=\{x\subset \lambda:| x| =\kappa \}\), \(D_{\kappa}\lambda =\{\{x,y\}:\) \(x,y\in P_{\kappa}\lambda\) and \(x\varsubsetneq y\}\).