[FOM] Reverse Mathematics

[Sam Sanders]

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