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). 
View on Springer
arxiv.org
5 Citations
Highly Influential Citations
1
Background Citations
3

5 Citations

Citation Type

Citation Type

The last forcing standing with diamonds
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.
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
TLDR
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
Sigma-Prikry forcing I: The Axioms
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…

References

SHOWING 1-10 OF 21 REFERENCES
SUCCESSOR OF SINGULARS: COMBINATORICS AND NOT COLLAPSING CARDINALS ≤ κ IN (< κ)-SUPPORT ITERATIONS SH667
On the one hand we deal with (< κ)-supported iterated forcing notions which are (E0, E1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly…
Fusion and large cardinal preservation
Sheva-sheva-sheva: Large creatures
We develop the theory of the forcing with trees and creatures for an inaccessible λ continuing Rosłanowski and Shelah [15], [17]. To make a real use of these forcing notions (that is to iterate them…
Successor of singulars: Combinatorics and not collapsing cardinals ≤gk in (
AbstractOn the one hand, we deal with (<gk)-supported iterated forcing notions which are $$(\hat \varepsilon _0 ,\hat \varepsilon _1 ) - complete$$ , bearing in mind problems on Whitehead groups,…
The last forcing standing with diamonds
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…
Reasonable Ultrafilters, Again
TLDR
It is shown how reasonable ultrafilters can be killed by forcing notions which have enough reasonable completeness to be iterated with lambda-supports (and the appropriate preservation theorem) is shown.
Reasonably complete forcing notions
TLDR
It is shown that it is consistent that dominating numbers associated with two normal filters on lambda are distinct, and more properties of forcing notions which imply that their lambda-support iterations are lambda-proper are introduced.
On iterated forcing for successors of regular cardinals
We investigate the problem of when $\leq\lambda$--support iterations of $<\lambda$--complete notions of forcing preserve $\lambda^+$. We isolate a property -- {\em properness over diamonds} -- that…
Measurable cardinals and the cofinality of the symmetric group
Assuming the existence of a hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinalsuch that 2 • = • ++ and the group Sym(•) of all permutations ofcannot be written as…
LORDS OF THE ITERATION
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),…
...
1
2
3
...