FOM: Hilbert's 5th Problem

[Moshe' Machover]

Colin McLarty writes:

> I don't know the Montgomery-Zippin solution myself.

Perhaps you do know Hirschfeld's solution (Trans AMS vol 321, pp379-400, 
1990), which uses nonstandard analysis. It is *much* shorter, very elegant, 
and includes some beautiful insights into the microstructure of topological 
groups without small subgroups.

This is a nice example of how a branch of *applied* model theory, which 
originated in f.o.m., can illuminate an important (and in *some* sense 
foundational) piece of mainstream maths.

I'd be interested to hear FOM contributors' views on the foundational
status of nonstandard analysis.

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