Kleene himself never stated that Turing had made a mistake in his paper, important in its own right for helping to establish the unsolvability of problems in group theoretic computations, although corrections to Turing's paper were also made later by Boone who originally pointed out "points in the proof require clarification, which can be given"  and Turing's only phd student, Robin Gandy. That Kleene doesn't mention this mistake in the body of his textbook where his presents his work on Turing machines but buried the fact he was correcting Alan Turing in the appendix was appreciated by Turing himself can be surmised from the ending of Turing's last publication "Solvable and Unsolvable Problems" which ends not with a bibliography but the words,
So countercyclical fiscal policy can be effective if any one of the conditions necessary for the equivalence does not hold. Controlling the real economy is possible perhaps even in a Keynesian style if government regains its potential to exert this control. Therefore, actually, new classical macroeconomics highlights the conditions under which fiscal policy can be effective and not the inefficiency of fiscal policy. Countercyclical aspirations need not to be abandoned, only the playing-field of economic policy got narrowed by new classicals. Keynes urged active countercyclical efforts of fiscal policy and these efforts are not predestined to fail not even in the new classical theory, only the conditions necessary for the efficiency of countercyclical efforts were specified by new classicals. Ricardian equivalence underlines the importance of fiscal reforms, since such reforms are needed in order to change the path of government expenditures. When implementing comprehensive fiscal reforms which make public sector more efficient governments do not exert countercyclical efforts of course, but form the necessary conditions for regaining countercyclical potential. In this respect, Ricardian equivalence clarifies the exact conditions necessary for countercyclical fiscal policies. 
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