Abstract:
It is well-known by now that large parts of (non-constructive)
mathematical reasoning can be carried out in systems 
which are
conservative over primitive recursive arithmetic PRA (and even much
weaker systems). On the other hand there are principles S of elementary
analysis (like the Bolzano-Weierstraß principle, the existence of a limit
superior for bounded sequences etc.) which are known to be equivalent to
arithmetical comprehension (relative to ) and therefore go far
beyond the strength of PRA (when added to ).
In this
paper we determine precisely the arithmetical and computational strength (in
terms of optimal conservation results and subrecursive characterizations of
provably recursive functions) of weaker function parameter-free schematic
versions S
of S, thereby exhibiting different levels of
strength between these principles as well as a sharp borderline between
fragments of analysis which are still conservative over PRA and
extensions which just go beyond the strength of PRA
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