FOM: the blind spot about theory-completeness and categoricity

Kanovei kanovei at
Tue Dec 16 12:42:03 EST 1997

>From: Neil Tennant <neilt at>
>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.

Vladimir Kanovei

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