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In $\forall x{\Big (}R(g(x))\vee \exists yR(x,y){\Big )}\iff \exists f\forall x{\Big (}R(g(x))\vee R(x,f(x)){\Big )}$ it is not clear what the $R(g(x))$ disjunct is.

It implies that R has both a unary and binary syntax, which is confusing, and the meaning of g is never explained. It seems to me that the formula would be simpler and still correct if it were written as $\forall x\exists yR(x,y)\iff \exists f\forall xR(x,f(x))$ If this is not correct, could you clarify the page? Thanks.

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