Composition theorem for generalized sum

Alexander Rabinovich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)137-167
Number of pages31
JournalFundamenta Informaticae
Volume79
Issue number1-2
StatePublished - 2007

Keywords

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

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