## Abstract

Let T be a complete theory of linear order; the language of T may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic countable models of T is either finite or 2^{ω}. (ii) If the language of T is finite then the number of nonisomorphic countable models of T is either 1 or 2^{ω}. (iii) If S_{ 1}(T) is countable then so is S_{ n}(T) for every n. (iv) In case S_{ 1}(T) is countable we find a relation between the Cantor Bendixon rank of S_{ 1}(T) and the Cantor Bendixon rank of S_{ n}(T). (v) We define a class of models L, and show that S_{ 1}(T) is finite iff the models of T belong to L. We conclude that if S_{ 1}(T) is finite then T is finitely axiomatizable. (vi) We prove some theorems concerning the existence and the structure of saturated models.

Original language | English |
---|---|

Pages (from-to) | 392-443 |

Number of pages | 52 |

Journal | Israel Journal of Mathematics |

Volume | 17 |

Issue number | 4 |

DOIs | |

State | Published - 1 Mar 1974 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics