## A technical result

April 25, 2011 at 15:36 | Posted in Uncategorized | Leave a commentThis post is concerned with a cosmetic reformulation ; I may add the proof later on when I get some time (mainly to make sure it’s all formulated exactly right), but the argument is a straightforward one.

Anyway, let us suppose and are regular cardinals, and .

We define the to consist of all cardinals for which there is a cardinal , a -complete ideal on , and a sequence of regular cardinals below such that

- for each , and
- .

Notice that the above definition is tailored to guarantee

On the other hand, the set consists of all cardinals such that

where

- is a progressive set of regular cardinals cofinal in ,
- ,
- is a -complete ideal on containing the bounded subsets of , and
- exists.

Proposition 1With notation as above, we haveand so

We will tend to use the above result as a definition in the future.

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