[FOM] Count Arithmetic
friedman at math.ohio-state.edu
Sat Jun 14 13:55:44 EDT 2003
Reply to Taylor 4:34PM 6/14/03:
>I was very impresed with Harvey Friedman's account of induction-free
>Count Arithmetic; and the fact that it turns out to be co-eval with
>(induction-full) PA. Very significant IMHO!
You show remarkable judgment (smile).
>There is one point I didn't really get, though.
>> 4. Various equality axioms. Besides the completely obvious, there is
>> the one that asserts that #(A,x1,...,xk;y) depends only on just what
>> x1,...,xk are such that A holds of x1,...,xk.
>I couldn't quite decipher this. Could Harvey or elseone please elaborate
>on this axiom and tell me what it actually does.
Suppose for all x1,...,xk, A(x1,...,xk) iff B(x1,...,xk). Then for
all y, #(A,x1,...,xk;y) iff #(B,x1,...,xk;y).
I owe Tennant a reply. This will come later.
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