[FOM] Re: Constructive analysis

Bas Spitters spitters at cs.kun.nl
Thu Sep 5 05:02:18 EDT 2002

Dear Steve,

May I suggest to look at:
Bridges & Richman, "Varieties of constructive mathematics"
to start with.

The picture that is painted there is the following:

     \         |           /

CLASS is classical mathemathics
INT is intuitionistic mathematics
RUSS is Russian recursive constructive mathematics
BISH is Bishop-style mathematics

So BISH is the common core.

The books suggested by the other participants of this list fall into either 
RUSS (B.A. Kushner)
or TTE (M.Pour-El,J. Richards, Weihrauch)
Where TTE is Weihrauch's system.

In fact, RUSS ~ BISH + CT + MP.
[ CT is Church's thesis, MP is Markov's thesis]

Similarly, TTE ~ BISH + CC + MP +FT.
[ CC is continuous choice, FT is the fan "theorem"]

Both of these similarities should be understood by a realizability 
interpretation. Since TTE is based on classical logic, the interpretation is 
not complete, but it is still a very convenient way to understand large parts 
of the theory.

Bas Spitters

Department of Computer Science, University of Nijmegen.
P.O.box 9010, NL-6500 GL Nijmegen, The Netherlands.
e-mail: spitters at cs.kun.nl  Phone: +31-24-3652610.

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