[FOM] Reverse Mathematics
Sam Sanders
sasander at cage.ugent.be
Tue Apr 16 02:05:47 EDT 2013
Dear members of the FOM,
In his book SOSOA, Steve Simpson makes the following well-known claim
regarding the big five systems of Reverse Mathematics:
<begin claim>
For a theorem T of ordinary mathematics, we have the following with few exceptions:
Either T is provable in RCA_0 or RCA_0 proves that T is equivalent to another one
of the big five systems.
<end claim>
Obviously, people will disagree on what exactly means "few exceptions".
However, I was wondering about the following:
a) Are there (any/many) people who *completely* reject Simpson's claim?
(Complete rejection means: it is false even for very liberal interpretations of "few exceptions")
b) What are their motivations for this rejection?
Best,
Sam Sanders
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