## A constructive, continuous solution to Hilbert's 17th problem, and other results in semi-algebraic geometry |

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### Contents

A Finiteness Theorem for Open SemiAlgebraic Sets | 29 |

IH The Continuous Constructive Solution | 39 |

Continuous Sums of Squares of Forms | 51 |

Copyright | |

2 other sections not shown

### Common terms and phrases

Archimedean Archimedean property Artin bad points bad set binary forms Bochnak Brumfiel C K[X Cassels Cauchy sequences Chapter Choi and Lam closure coefficients computational topology Conjecture construct continuous functions Corollary Dedekind cut defined denominator discontinuous Efroymson Ellison filter finite union Finiteness Theorem form of degree formal power series Geometry hence Hilbert's 17th Problem homogeneous implies indeterminate Kreisel Kreisel's question Landau Lemma lowest degree Math Model Theory non-empty nonnegative open s.a. set ordered field Pfister Positivstellensatz primitive recursive proof of 2.1 prove psd forms psd polynomials quadratic form quaternary quartic rational functions real algebraic real closed field replaced representation resp Ressel result retraction Reznick Rn+1 Robinson s.a. functions Semi-Algebraic showed SOS-representation Stengle's Theorem strictly definite subfield subset summands Sums of Squares symmetric Tarski-Seidenberg Theorem tion U{gi union of U's unique orderability usual topology variables W{gi X-degree X-homogeneous inclusion Zariski dense zero