## Recursive functionals of arguments of finite type |

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3'-ec-tree for z,B B*-tree Cartesian products clause closure conditions composition computation tree cons for z,B considered consistent oracle define v(t+2 defined and equal Degrees of Unsolvability domain ec for w,C ec for z,B ec or cons ec-wfd for z,B embedded equivalence relation exactly finite sequence finite subset follows function defined function h function with index Godel number h e F(uq Hence index with variables initial function initial segment Ix(z Kleene Kleene's lemma list of variables minimal degree Note notion object of type partial functions partial recursive function predicate primitive recursive function proceed Proof Q is recursive recursion theorem recursive in fo regular result satisfies say that z}(B schema schemata sequence of functions Set c(g,z w,p special triple Subcase substitution index suppose triple uo type r-1 undefined universal quantifier upper semi-lattice v(n+l v(t+l variables of type well-founded with respect wfd for z,B xJ+1