Hechler's Theorem for tall analytic P-ideals

Abstract

We prove the following version of Hechler's classical theorem: For each partially ordered set (Q,≤) with the property that every countable subset of Q has a strict upper bound in Q, there is a ccc forcing notion such that in the generic extension for each tall analytic P-ideal ℐ (coded in the ground model) a cofinal subset of (ℐ,⊆^*) is order isomorphic to (Q,≤).