## Abstract

Composition theorems are tools which reduce sentences about some compound structure to sentences about its parts. A seminal example of such a theorem is the Feferman-Vaught Theorem [3] which reduces the first-order theory of generalized products to the first order theory of its factors and the monadic second-order theory of index structure. Shelah [23] used the composition theorem for linear orders as one of the main tools for obtaining very strong decidability results for the monadic second-order theory of linear orders. The main technical contribution of our paper is (1) a definition of a generalized sum of structures and (2) a composition theorem for first-order logic over the generalized sum. One of our objectives is to emphasize the work-out of the composition method.

Original language | English |
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Pages (from-to) | 137-167 |

Number of pages | 31 |

Journal | Fundamenta Informaticae |

Volume | 79 |

Issue number | 1-2 |

State | Published - 2007 |

## Keywords

- Composition Theorem
- Decidability
- Expressibility
- First-order logic