## [Sh:430.1-3] Elementary Submodel Conventions

January 27, 2011 at 18:39 | Posted in Uncategorized | Leave a commentWe’re going to be working with elementary submodels a lot, so I wanted to pin down the assumptions we make and the notation we use.

In the current project, we are investing combinatorics relevant to a singular cardinal , and is a regular cardinal “much much larger” than . The exact identity of isn’t important. We also need to fix some well-ordering of ; we will build this into the structures we consider so that they all have definable Skolem functions.

In general, denotes some expansion of by at most countably many functions, constants, and relations. I won’t get too pedantic with this, but for example, in the current situation we want to contain a name for , so that we know makes it into any elementary submodel of . We won’t make this explicit in our notation.

I will use (or just ) to denote the Skolem hull of in the structure .

I may update this post to reflect new things that I forgot to include…

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