Strong Cardinals and Sets of Reals in L_ω1(ℝ)

Abstract

We generalize results of [3] and [l] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reds in &(R) is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals. Mathematics Subject Classiflcation: 03335, 03345, 03355.

The core model for almost linear iterations

“…The proof of the following lemma 8.13 needs some care in order to not to go beyond the bounds of predicative class theory. We shall need the following auxiliary concept, which was introduced in [4, Definition 2.7] (and generalizes a concept of [8]; see also [24]). It is straightforward to check that the proof of [4, Lemma 2.9] works below 0 | • ; this observation establishes:…”