These days, Peano Arithmetic ($PA$) refers to the first-order version of the axioms, where induction is only over formulas referring to natural number variables. Peano's original version of the ...
Hello. I already asked the question here. The main point is that I tried to prove in Primitive recursive arithmetic (PRA) the totality of the Ackerman function, and I found, that the single thing ...
It is known that to prove completeness of first-order logic for countable languages WKL0 is enough. But, is it the weakest subsystem where one can prove it? What about the incompleteness theorems? Is ...
According to the Wikipedia ACA0 is a conservative extension of First Order logic + PA. http://en.wikipedia.org/wiki/Reverse_Mathematics First of all I have a few questions about the proof: a - What ...