# More about λ-support iterations of (

@article{Roslanowski2013MoreA, title={More about $\lambda$-support iterations of (}, author={Andrzej Roslanowski and Saharon Shelah}, journal={Archive for Mathematical Logic}, year={2013}, volume={52}, pages={603-629} }

This article continues Rosłanowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) 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).

## 5 Citations

The last forcing standing with diamonds

- MathematicsFundamenta Mathematicae
- 2019

This article continues Roslanowski and Shelah math.LO/9906024 and 1105.6049 We introduce here yet another property of (<lambda)-strategically complete forcing notions which implies that their…

Explicit example of collapsing kappa^+ in iteration of kappa-proper forcings.

- Mathematics
- 2018

We give an example of iteration of length omega of (<kappa)-complete kappa^+-cc forcing notions with the limit collapsing kappa^+. The construction is decoded from the proof of Shelah [Proper and…

A parallel to the null ideal for inaccessible $$\lambda $$λ: Part I

- MathematicsArch. Math. Log.
- 2017

A positive answer for a generalization of the null ideal for a “mild” large cardinal $$\lambda $$λ—a weakly compact one is found and it is shown that this together with the meagre ideal behaves as in the countable case.

Regularity properties on the generalized reals

- MathematicsAnn. Pure Appl. Log.
- 2016

Sigma-Prikry forcing I: The Axioms

- MathematicsCanadian Journal of Mathematics
- 2020

Abstract We introduce a class of notions of forcing which we call
$\Sigma $
-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of…

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The last forcing standing with diamonds

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This article continues Roslanowski and Shelah math.LO/9906024 and 1105.6049 We introduce here yet another property of (<lambda)-strategically complete forcing notions which implies that their…

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We introduce several properties of forcing notions which imply that their �-support iterations are �-proper. Our methods and techniques refine those studied in (RS01), (RS07), (RS05) and (RS),…