## Recursive and simple vector spaces |

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### Contents

1 Introduction and notation | 2 |

3 Splitting theorems | 7 |

4 Bases for r e spaces | 16 |

3 other sections not shown

### Common terms and phrases

algebraic assume b2s+l closure operator coinfinite r.e. set contradiction Cornell University Corollary define definition of simple Dekker dependence degree dim(I mod dimensional r.e. space dimensional vector space direct sum enumerable vector space extends a result finite dimensional spaces finite subsets following theorem fully extendible basis fully extendible spaces godel numbers Hence hyperhyper hyperhypersimple hh-simple infinite dimensional r.e. infinite field infinitely many stages Kalantari lattice of recursively lattice theoretic least element Let A,B Let F linear span main theorem Metakides and Nerode mod(A modulo n>j n Nerode 12 Proof of lemma proof of Theorem r.e. bases r.e. independent set r.e. nonrecursive space r.e. vector spaces Recall recursive set recursive space recursively enumerable sets requirement of higher satisfy set of vectors sets of integers simple set simple space SIMPLE VECTOR SPACES splitting theorem superspaces Turing degree weak array