[FOM] multi-sorted logic

Richard Heck rgheck at brown.edu
Mon Mar 13 21:25:30 EST 2006

> In response to the point raised both by A Hazen and R Heck, that there 
> is little to multi-sorted logic over and above standard one-sorted 
> predicate logic, I believe that early work by Feferman on the 
> interpolation in multi-sorted contexts (also referred to by Hazen) shows
> that this is not quite the case.
Thanks to Aldo for this lead.

A quick google search led me to some papers by Martin Otto, including
one from the /Bulletin of Symbolic Logic/ 6 (2000), pp. 447-62, also
available here:
This one proves various versions of interpolation theorems in
many-sorted contexts. Feferman's papers on this topic appear to be
fairly inaccessible. Another that seems important and is easily had is
Jacques Stern, "A New Look at the Interpolation Problem", /Journal of
Symbolic Logic/ 40 (1975) , pp. 1-13, which is on JSTOR.

In the little bit of reading I did, I found several people remarking on
the "strength" of these results and contrasting them, in ways I didn't
quite understand, with the interpolation theorems for single-sorted
logic. Can anyone provide a sketch of the details? Here again, the
papers to which people usually refer as containing important
applications of this result are pretty inaccessible, at least from where
I am.


Richard G Heck, Jr
Professor of Philosophy
Brown University
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