Significant fragments of classical analysis
Victor Harnik

ABSTRACT
Classical analysis can be developed in a certain strong fragment of
second order arithmetic (this fragment is sometimes called, simply,
"analysis").  The full strentgh of "analysis" is rarely needed for the
most important theorems and a line of research initiated by Friedman,
is concerned with the question of determining precisely the subsystem
of analysis needed to prove particular theorems.  Certain important
fragments of analysis have been singled out and their relation to
various results of analysis clarified. I will give a survey of the
subject and will conclude by outlining a new proof of a theorem of
Harrington, concerned with the relationship between two fragments of
analysis called "Weak Koenig Lemma" and "Recursive Comprehension
Axiom".