FOM: the blind spot about theory-completeness and categoricity
kanovei at wminf2.math.uni-wuppertal.de
Tue Dec 16 12:42:03 EST 1997
>From: Neil Tennant <neilt at hums62.cohums.ohio-state.edu>
>What I would dearly like to know is whether this "blind spot" was
>genuine and widespread, or whether there was *any* logician publishing
>at that time, no matter how little-known or in how remote a place, who
>said or published anything during the years 1918-1933 that could be
>taken as evidence of a suspicion that theory-completeness and categoricity
>could not simultaneously be achieved (no matter what logic and
>language one used).
Luzin (1925) wrote that (approximately) it is not known
and will never be known whether all projective sets are
L measurable. Hausdorff wrote something like this (about
other problems) even earlier (maybe 1908).
In Neil Tennant's language this can possibly be rendered as:
whichever way they manipulate (or will manipulate)
with the "deductive power", the "expressive/descriptive
power" will suit to some natural mathematical statements.
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