FOM: OBT

[Kanovei]

>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 
seem somewhat paradoxical, 
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). 

Vladimir Kanovei