Is the $\Sigma_{n}$-recursion supported by $\Sigma_{n}KP=KP+\Sigma_{n}$-separation + $\Sigma_{n}$-collection equivalent with $\Sigma_{n}$ transfinite recursion? If not, how do these notions differ?
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asked Dec 11, 2014 at 15:40
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2$\begingroup$ Could you clarify what you mean by "$\Sigma_n$ recursion" and "$\Sigma_n$ transfinite recursion"? $\endgroup$– François G. DoraisCommented Dec 11, 2014 at 17:11
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$\begingroup$ Cfr. the answer to my question here: mathoverflow.net/questions/188214/… $\endgroup$– Frode Alfson BjørdalCommented Dec 12, 2014 at 8:47
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$\begingroup$ And by "$\Sigma_n$ transfinite recursion" you mean the restriction to ordinals? Since both are consequences of $\Sigma_nKP$, what do you mean by "equivalent"? $\endgroup$– François G. DoraisCommented Dec 13, 2014 at 2:24
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$\begingroup$ By $\Sigma_{n}$ transfinite recursion I meant transfinite recursion restricted to $\Sigma_{n}$ functions. If both these are consequences of $\Sigma_{n}KP$, that is equivalent enough for me. :) $\endgroup$– Frode Alfson BjørdalCommented Dec 13, 2014 at 7:37
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