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Consider the following theorem about Heyting arithmetic (HA): For every arithmetical formula $\phi$ whose only free variable is $n$, if $\text{HA} \vdash \forall n. \phi \lor \lnot \phi$ and $\text{...

$\def\f#1{\text{#1}}$Does $\f{ACA}$ prove that any two internally complete ordered fields are isomorphic? Here internal completeness is expressed roughly as "every sequence of reals with an upper ...

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 ...

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 ...