## Representations of Indifference Relations |

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### Contents

Preliminaries | 1 |

Finite Indifference Systems | 16 |

Compatibility with a Weak Order | 42 |

6 other sections not shown

### Common terms and phrases

adjacency matrix adjacent algorithm Appendix axioms binary relation c.Ic cardinality Chapter compatible simple order complete partite graphs condition converse countable define definition denote dim G dim S(n dimension embedded equivalence relation equivalent points extremal in G finite graph finite indifference system follows function f G is weakly Goodman system graph A,I graph G implies interval graph irreflexive Lekkerkerker lemma Luce matrix n-space non-adjacent extreme points notion of indifference order-isomorphic oriented graph point of G primitive cycle proof of theorem prove Q.E.D. Corollary Q.E.D. Remark real line real-valued function representable by jnds result rigid-cycle graph satisfies Scott and Suppes semiorder strongly representable structure theorem subset Suppose A,P Suppose G symmetric complement symmetric complementary symmetric graph theorem 2.1 triple point weak components weak extreme point weak indifference system weak order weakly connected graph weakly connected subgraph weakly representable whence