## Arithmetic degrees: initial segments, [omega]-REA Operators and the [Omegal]-jump |

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### Contents

Preliminary results | 10 |

Incomparable WREA sets | 20 |

The range of the wjump on degrees below W | 42 |

4 other sections not shown

### Common terms and phrases

2m+l a-degrees Abraham and Shore Abraham-Shore act at stage analog AQ(X argument arithmetic degrees arithmetic singletons arithmetic tree calculate canonical index Chapter codes a standard coinfinite column n+1 computation construction of column converges Corollary 2.2 defined Definition degrees of unsolvability dense sets diagonalization e-splitting tree effectively codes elementarily equivalent embedding enumeration of column exact pair finite injury forcing given hence implies incomparable w-REA sets induction initial segments input isomorphic Jockusch and Shore jump classes lattice least element Lemma metic minimal pair negative requirements notation Note Odifreddi permanently restrains proof Proposition Q acts r.e. operation r.e. sets recursion theorem recursive function result Sacks Jump Theorem sequential table set r.e. set w-REA stage s+1 standard model string Suppose T A(X Theorem 2.3 Turing degrees Turing equivalences Turing jump Turing reducibility uniform uniformly w-generic w-jump w-REA operator wants to put Z,B,C-lemma