[FOM] Finite axiomatisation
pax0@seznam.cz
pax0 at seznam.cz
Sun Aug 24 07:03:15 EDT 2008
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.
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