## Descriptive set theory and forcing: how to prove theorems about Borel sets the hard way |

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### Contents

On the length of Borel hierarchies | 7 |

Abstract Borel hierarchies | 11 |

Characteristic function of a sequence | 13 |

Copyright | |

32 other sections not shown

### Common terms and phrases

argument Aronszajn tree assume Baire basic clopen set Borel hierarchies Borel set Borel(2 Claim clopen sets closed set Cohen real compatible complete boolean algebra Consequently construction contains a perfect Corollary countable set countable unions define dense set descriptive set theory disjoint domain(p elements equivalence classes equivalence relation finite follows G Fp ground model Harrington Hausdorff space hence homeomorphic hyperarithmetic iff there exists implies incompatible induction intersections isomorphic K-Borel set Kunen Lemma limit ordinal Louveau Louveau's Theorem Luzin set meager sets nonempty Note oid(X open sets open subsets ord(X P-generic partial order perfect set poset proof of Theorem prove rank function rank(p real model recursive separable metric space sequence set coded subsets of uw Suppose for contradiction terminal node tree T C uncountable well-founded trees well-ordering WF<a