Blowing up Power of a Singular Cardinal –wider Gaps

Blowing Up the Power of a Singular Cardinal

Silver type theorems for collapses

The classical theorem of Silver states that GCH cannot break for the first time over a singular cardinal of uncountable cofinality. On the other hand it is easy to obtain a situation where GCH breaks on a club below a singular cardinal κ of an uncountable cofinality but 2 = κ. We would like here to investigate the situation once blowing up power of singular cardinals is replaced by collapses of...

On gaps under GCH type assumptions

We prove equiconsistency results concerning gaps between a singular strong limit cardinal κ of cofinality א0 and its power under assumptions that 2 κ = κ+δ+1 for a cardinal δ < κ and some weak form of the Singular Cardinal Hypothesis below κ.

Blowing up The Power Set of The Least Measurable

We prove some results related to the problem of blowing up the power set of the least measurable cardinal. Our forcing results improve those of [1] by using the optimal hypothesis.

Short extenders forcings – doing without preparations

We introduce certain morass type structures and apply them to blowing up powers of singular cardinals. As a bonus, a forcing for adding clubs with finite conditions to higher cardinals is obtained.