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1-generic algebra algorithm automata axioms basic sets binary Boolean bounded c)-conservative closure closure algebra complete construction contiguous degrees continuous Corollary countable decision problem defined definition denote elements equivalent example exp exp explicit fact final topology finite graphs finite structures finitely approximable first-order logic fixed point formal formula free variables function f given global predicates Hence implies induction infinite initial segment integers iteration Kleene language least fixed point Lemma Math mathematical matroids mergesort monotone Moschovakis natural numbers Nerode notion operative order type pair parallel programs partial function polynomial predicate variable problem proof of Theorem properties provable prove PTIME PTIME computable r.e. degrees r.e. sets recursion spaces recursion theory recursive functions recursively enumerable relation representation requirements rules satisfies second-order logic semantics sentence sequence star-finite strings subsets Suppose symbol Theorem topology tuple Turing degrees