Ideals on P\kappa\lambda which does not depend on large cardinals

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The basic concepts of the structural theory of ideals on P_{\kappa}\lambda, P-points, Q-points, and selective ideals are defined, and several theorems are proved, some of which hold similarly for ideals on \kappa, whereas the others are very different from those on \kappa. We get several facts which says that some theorems on \kappa result from the special situation that \kappa=\lambda.It has been long known that the stationary sets of P_{\kappa}\lambda reflects when \kappa is supercompact. We construct a forcing model in which \kappa is strongly compact and P_{\kappa}\lambda has a stationary set without such reflection.