Recursive Functions Modulo Co-maximal Sets |
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arithmetic Assume Clearly co-maximal construction contains an infinite contradicting the assumption CORN CORNELL CORNEL UNIVERSITY CORNELL LIBRARY CORNELL CORNELL LIBRARY UNIVERSITY CORNELL UNIVERSITY LIBRARY Corollary dominates every recursive elements exists EZRA CORNELL f and g f(M₁ f(yo finite function f function with range Gödel number hence i-retains implies infinite number integers k₁ k₂ k₂-holds Lachlan Lemma Let f LIBRARY CORNELL UNIVERSITY LIBRARY LIBRARY M₁ M₂ a.e. major subset many-one reduction marker maximal set minimal many-one degrees mo(s non-standard non-standard models one-one otherwise P₁ partial recursive functions Proof Proposition 2.1 QE{e r-maximal set r.e. set r.e. Turing degree R/M₁ R/M₂ REC set recursion theory recursive isomorphism recursive set s₁ s₁(x set containing set of degree SITY Skolem functions stage s,a,b Theorem 5.1 Turing reducible u₁ UNIV UNIVERSITY CORNELL CORNELL UNIVERSITY LIBRARY CORNELL v₁ vino x:fog(x zero divisors Σ Σ є М хо