## Non-Greek mathematics |

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### Contents

Foreword | iv |

Hilbert ideas in mathematics and its related topics 1 | iv |

Higher order many sorted theories | 16 |

Copyright | |

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### Common terms and phrases

a b c affine plane algebraic axiom system called cardinal commutative completes the proof complex numbers consider contains contradiction Corollary define Definition denoted Desargues Desargues Small Theorem element elementary Euclidean geometry example exists exactly Figure finite decomposition formal theory formally real formula free ultrafilter Hence Hilbert Hjelmslev ring hm(t holds implies infinite set involution irreducible polynomial isomorphic Lemma line passing linear 2-normed space mathematical induction maximal ideal mereology metric plane natural numbers non-Archimedean non-Archimedean field notion ordered field ordered group Pasch axiom perpendicular pole polynomial projective Hjelmslev plane prove Pythagorean field rational numbers real closed real closed field real field real numbers relation satisfies Sb(A shows skew field subset sum of squares suppose symbols Theorem theorem of three triangle trivial ultrapower ultraproduct vector space