## Recursive functions modulo co-maximal sets |

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### Contents

A NECESSARY AND SUFFICIENT CONDITION FOR | 5 |

SKOLEM FUNCTIONS FOR THE TRUE SENTENCES | 21 |

THE E SETS OF rfM | 31 |

2 other sections not shown

### Common terms and phrases

Assume f certainly defined co-maximal cofinite cohesive set constant function contains an infinite contradicting the assumption define a recursive degree a_ denote dominates every recursive E E k+1 elementarily equivalent elementary theory elements exists f and g function f function with range go to stage Godel number i-holds i-resembles implies incomparable many-one degrees infinite number infinite retraceable subset infinitely many x e integers Lachlan Lemma Let aQ Let f major subset many-one reduction maximal set maximal superset minimal many-one degrees non-standard models Note order of magnitude otherwise partial recursive functions Proof Proposition 2.1 prove r-maximal set r.e. set r.e. Turing degree range of f recursion theory recursive isomorphism recursive set set of degree sets have minimal setting k<s,a,b si(x Skolem functions stage s,a,b suffices to show sufficiently large Theorem 5.1 Turing reducible x e M2 y e range zero divisors