## Some Assumptions

March 28, 2012 at 13:33 | Posted in Uncategorized | Leave a commentI have been contemplating exactly where to begin the discussion of these matters, and I think that I want to go back to Chapter VIII of The Book, and look at the first section of it because the arguments there keep appearing in later works.

In this post, I’m going to write down some assumptions [(a)-(e) of Claim 1.2] that will be used in the next few posts.

**The Assumptions**

We assume the following

- is a set of regular cardinals satisfying
- For every , we let satisfy
- ,
- is strictly increasing modulo ,
- if and , then for each we have
- for every and , there is a such that (everwhere)

- is a sufficiently large regular cardinal, is a well-ordering of
- is an increasing continuous sequence of elementary submodels of such that
- and .

I’m going to do some “dictionary work” to get the official names for such objects. I just want to check which terms have become standard, and I’ll use the Abraham/Magidor Handbook article as the final word.

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