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Basic Introductory Results

In: A Course on Basic Model Theory

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Listed:
  • Haimanti Sarbadhikari

    (Indian Statistical Institute, Stat-Math Unit)

  • Shashi Mohan Srivastava

    (Indian Statistical Institute, Stat-Math Unit)

Abstract

The goal of this chapter is to present basic introductory techniques of model theory. The main results presented are $$\L $$ oś fundamental lemma on ultraproduct of structures, compactness theorem and quantifier elimination. These are cornerstones of model theory. A large number of applications given in this chapter bear testimony to the importance of these results. We also introduce the notion of independence and dimension in minimal sets. Finally we give several applications of the results proved in this section in algebra and geometry. A large number of examples and exercises are given as we go along.

Suggested Citation

  • Haimanti Sarbadhikari & Shashi Mohan Srivastava, 2017. "Basic Introductory Results," Springer Books, in: A Course on Basic Model Theory, chapter 0, pages 45-84, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-5098-5_2
    DOI: 10.1007/978-981-10-5098-5_2
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