## Strategy and assumptions

May 10, 2011 at 16:21 | Posted in Uncategorized | Leave a commentIn this post, we’ll lay out the notation and strategy for the proof.

Let us assume , , , and are cardinals with

such that

whenever and satisfy

- is a progressive set of regular cardinals with and ,
- is a -complete ideal on extending the bounded ideal, and
- the structure has a true cofinality.

To save ourselves some time later, let us agree to call such and *relevant*.

Now let be a sufficiently large regular cardinal, and let be an elementary submodel of satisfying

- ,
- , and
- is an ordinal of cofinality greater than .

Our goal is to show that the collection

witnesses , i.e., that every set in can be covered by a union of fewer than sets from .

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