# FOM: OBT

Kanovei kanovei at wminf2.math.uni-wuppertal.de
Sun Dec 14 15:30:00 EST 1997

>From: Solomon Feferman <sf at csli.stanford.edu>

>what
>people think of OBT and how it might affect what we think of restricting
>to the mathematics of Borel sets.  Is this a sign of deep pathology
>infecting set theory, or is it just a sign that one should not rely on
>one's intuitions when it comes to the concepts involved, or what...?
>(Guess where I might come out on this.)

Constructions like
(1) a meager F_\sigma set of full measure, and
(2) the more complicated example for OBT
because "big" in one sense becomes "small" in the other
equally reasonable sense. However it would be very
difficult (or impossible) to separate mathematical
tools leading to (1) (if not to (2)) from those used in
the measure theory, for example. A curious associated
question is: why there exist only two reasonable notions
of "bigness" (measure and category).