FOM: Neo-Fregean reverse mathematics

[Alasdair Urquhart]

Following on from Charles Parsons's and Allen Hazen's
postings, let me try to make my earlier query more precise.
Let PA2 (2nd order Peano arithmetic) and FA be as in 
Allen Hazen's posting.  Then it appears that they
are mutually interpretable.  Now is the stronger claim
true that they are synonymous?  Here I am taking
"synonymous" to be defined as in the paper of Karel
de Bouvere ("Theory of Models", ed. by Addison, Henkin
and Tarski, 1965, p. 402).  If they are not, then
they provide an interesting non-artificial example of
two mutually interpretable theories that are not
synonymous (De Bouvere mentions an unpublished example
of this phenomenon due to David Kaplan).

--Alasdair Urquhart