Iteration ofλ-complete forcing notions not collapsingλ+

Iteration of λ-complete forcing notions not collapsing λ

We look for a parallel to the notion of " proper forcing " among λ-complete forcing notions not collapsing λ +. We suggest such a definition and prove that it is preserved by suitable iterations. This work follows [Sh 587] and [Sh 667] (and see history there), but we do not rely on those papers. Our goal in this and the previous papers is to develop a theory parallel to " properness in CS itera...

More about λ-support iterations of (<λ)-complete forcing notions

This article continues Ros lanowski and Shelah [8, 9, 10, 11, 12] and we introduce here a new property of (<λ)–strategically complete forcing notions which implies that their λ–support iterations do not collapse λ (for a strongly inaccessible cardinal λ).

Simple Forcing Notions and Forcing Axioms

Complete forcing numbers of polyphenyl systems

The idea of “forcing” has long been used in many research fields, such as colorings, orientations, geodetics and dominating sets in graph theory, as well as Latin squares, block designs and Steiner systems in combinatorics (see [1] and the references therein). Recently, the forcing on perfect matchings has been attracting more researchers attention. A forcing set of M is a subset of M contained...

On Nicely Definable Forcing Notions

We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also show that amoeba forcing cannot be P(X)/I if I is an א1-complete ideal. Furthermore, we generalize the results of [12].