FOM: Delta one comprehension and constructivism

[Peter Smith]

I better preface this with the admission that I really am a beginner 
in this area. But here goes:

In Friedman/Simpson/Smith (Ann. Pure Applied Logic 25, 1983) the 
authors discuss why RCA_0 isn't going to be bought by the 
constructivist. For a start, it has a classical logic. But they also 
write:

"Yet another point of difference is that RCA_0 includes the Delta_0_1 
comprehension axiom. This axiom resembles a special case of Markov's 
principle and is therefore probably not acceptable to all 
constructivists."

I'm being dim and missing the resemblance. Why would a constructivist 
balk at countenancing recursive sets? [Put it this way: a 
constructivist mightn't like this or that base first-order theory. 
But if a base theory passes muster, can adding a commitment to just 
the recursive sets take us to a constructively unacceptable 
theory???.]

Any explanation gratefully received!

Peter Smith
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Dr Peter Smith
Jesus College, Cambridge CB5 8BL, UK
ps218 at cam.ac.uk