[FOM] Count Arithmetic

[Harvey Friedman]

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.

Harvey Friedman