FOM: RE: 153:Large cardinals as general algebra - sent again

Insall montez at
Mon Jun 17 19:02:20 EDT 2002

Hello Harvey,
     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
37(1991), 525-532.
3.  ``Some Finiteness Conditions in Lattices - Using Nonstandard Proof
Methods'', in J Austr Math Soc 53(1992), 266-280.

Matt Insall

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
it.  -MI

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