FOM: RE: 153:Large cardinals as general algebra - sent again
montez at rollanet.org
Mon Jun 17 19:02:20 EDT 2002
These are quite nice, and related to work I have done years ago, both
alone and with colleagues when I was a graduate student and an assistant
professor. Please see the following references:
1. ``Some Nonstandard Methods Applied to Distributive Lattices'', with M.
Gehrke and K. Kaiser. in ZML 36(1990), 123-131. (ZML is now MLQ)
2. ``Nonstandard Methods and Finiteness Conditions in Algebra'', in ZML
3. ``Some Finiteness Conditions in Lattices - Using Nonstandard Proof
Methods'', in J Austr Math Soc 53(1992), 266-280.
PS: The main item that caught my eye in your post is that you deal with
``localizations'', in terms of finite, countable, etc. generation of
subalgebras. In reference number 1, I dealt with the same things.
``Local'' versions of properties, and their nonstandard characterizations.
Since the compactness theorem plays a central role in the foundations of
nonstandard analysis, some of my results are likely to be either corollaries
of yours or equivalent to one or more of them. I will think about it a
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