[FOM] Count Arithmetic

[Bill Taylor]

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!

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.

TIA.

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        Bill Taylor                W.Taylor at math.canterbury.ac.nz
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The known is finite, the unknown is infinite.
We stand on an islet of comprehension in a limitless ocean of inexplicability.
                                Our business is to reclaim a little more land.
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