FOM: Re: 102:Turing Degrees/2

[Jeffrey Ketland]

Harvey Friedman:

>The following is a restatement of a theorem from Turing Degrees/1.
>
>Let Z2 be the usual first order system of second order arithmetic. Let Z2+
>be Z2 with a satisfaction predicate added and induction and comprehension
>are extended to all formulas in the expanded language.

Are the axioms you use for Sat(x,y) in Z2+ Tarski's inductive axioms?
Do you consider "self-applicative" (usually called Kripke-Feferman) axioms
in this context over Z2?
E.g., Things like the axiom
T-rep:  T(A) --> T(T(A)))
from Friedman/Sheard 1987?

More generally, if Ref(S) is Feferman's reflective closure operation on
system S (Fefermann 1991: "Reflecting on Incompleteness" 1991), do you know
how Ref(Z2) turns out? Proof-theoretic strength, interpretability?

Regards - Jeff


~~~~~~~~~~~ Jeffrey Ketland ~~~~~~~~~
Dept of Philosophy, University of Nottingham
Nottingham NG7 2RD United Kingdom
Tel: 0115 951 5843
Home: 0115 922 3978
E-mail: jeffrey.ketland at nottingham.ac.uk
Home: ketland at ketland.fsnet.co.uk
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~