## Independent Axioms for Minkowski Space-TimeThe primary aim of this monograph is to clarify the undefined primitive concepts and the axioms which form the basis of Einstein's theory of special relativity. Minkowski space-time is developed from a set of independent axioms, stated in terms of a single relation of betweenness. It is shown that all models are isomorphic to the usual coordinate model, and the axioms are consistent relative to the reals. |

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### Contents

Appendices | 8 |

Primitive notions and axioms | 9 |

Temporal order on a path | 18 |

Collinearity and temporal order | 31 |

Existence and properties of collinear sets | 53 |

Paths and optical lines in a collinear set | 78 |

Theory of parallels | 113 |

Onedimensional kinematics | 144 |

Independence models | 194 |

Veblens axioms for an ordered geometry | 212 |

Alternative axiom systems | 215 |

Open questions | 222 |

Notes to the chapters | 225 |

231 | |

233 | |

240 | |

### Common terms and phrases

affine applies Axiom axiomatic system belong bijection bounded called Chapter classes of parallels closest collinear set Collinearity Theorem completes concept consequence consider contains Continuity contradiction convergent coordinate system corresponding cross define definition denoted described direction discussed distinct events distinct paths divergent equations establish Euclidean Existence Theorem Figure follows geometry given implies the existence indexed induced inequality integer interval invariant isomorphism isotropy mappings kinematic triangle Lemma linear meets Minkowski space-time obtain optical line order relation orthochronous pair parallels path Q paths which meet plane points positive previous theorem proof properties rapidity record functions reflection Remark respectively result satisfied Second segment set of events set of paths side signal functions similar space specified statement subset symbols Theorem 13 Third translation Uniqueness unreachable set Veblen whence

### References to this book

Non-Euclidean Geometries: János Bolyai Memorial Volume János Bolyai,András Prékopa,Emil Molnár No preview available - 2006 |