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Semantics of First-Order Languages

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A Course on Mathematical Logic

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Abstract

In the last chapter, we presented syntactical notions pertaining to first-order theories. However, in general, mathematical theories are not developed syntactically. In this chapter, we give the semantics of first-order languages to connect the syntactical description of a theory with the setting in which a mathematical theory is generally developed. This chapter should also be seen as the beginning of a branch of logic called model theory, which can be thought of as the general study of mathematical structures. Some important notions from model theory, for example, the downward Löwenheim–Skolem theorem, types, homogeneous structures, and definability, are introduced here.

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Authors and Affiliations

  1. Indian Statistical Institute, Barrackpore Trunk Road 203, Kolkata, 700108, India

    Shashi Mohan Srivastava

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  1. Shashi Mohan Srivastava
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Srivastava, S.M. (2013). Semantics of First-Order Languages. In: A Course on Mathematical Logic. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5746-6_2

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