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A note on ”$${\mathcal E}^ 0_*={\mathcal E}^ 2_*$$” problem. (English) Zbl 0598.03035
We prove that the conjecture “$${\mathcal E}^ 0_*={\mathcal E}^ 2_*$$” is equivalent to the following assertion: the class $${\mathcal E}^ 0$$ is closed under the bounded recursion schema in which we define: f($$\vec x,y+1)=h(\vec x,y,f(\vec x,y),f(\vec x,y-1))$$ instead of the usual f($$\vec x,y+1)=h(\vec x,y,f(\vec x,y))$$.
##### MSC:
 03D20 Recursive functions and relations, subrecursive hierarchies
##### Keywords:
Grzegorczyk classes; bounded recursion
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