[FOM] Finite axiomatisation

[pax0@seznam.cz]

I react to the posting from Stephen G Simpson <simpson at math.psu.edu>
  
>  Yes, this is very much in the literature.  See for instance my book
>  "Subsystems of Second Order Arithmetic," where the significance of
>  ACA_0 in reverse mathematics and foundations of mathematics generally
>  is discussed.  There it is pointed out that ACA_0 is a finitely
>  axiomatizable conservative extension of PA, analogously to how NBGC is
>  a finitely axiomatizable conservative extension of ZFC.

where he points out that ACA_0 is finitely axiomatizable.
But I found a paper by Harvey Friedman, where he claims (on the 1. page) the opposite:
"RCA_0 cannot prove TST <--> ACA_0 since ACA_0 is not finitely axiomatizable."
The pdf can be found here:
http://www.math.ohio-state.edu/~friedman/pdf/BabyBRT100301.pdf
LECTURE NOTES ON BABY BOOLEAN RELATION THEORY

Where is the problem? Jan P.