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Peano Algebra and it's base theorem
Peano Algebra's are based on the following:
If a unary predicate P holds for 0, and if P holds, together with an element
x, also for it's succesor x', then P holds for all natural numbers.
The question under consideration is NOT an attempt to describe a language in
a Sigma structure/algebra/model. We are NOT trying to analyze the language
but rather a specific mathematical statement made IN that language.
They are not the same problem and hence Peano Algebra's do NOT apply.
Nice straw man, I had to drag a math book out to refresh what a Peano
Algebra was (don't think I've ever had to deal with one).
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