Finite model theory studies the expressive power of logics on finite models. Classical model theory, on the other hand, concentrates on infinite structures: its origins are in mathematics, and most objects of interest in mathematics are infinite, e.g., the sets of natural numbers, real numbers, etc. Typical examples of interest to a model-theorist would be algebraically closed fields (e.g., 〈ℂ, +, •〉), real closed fields (e.g., 〈ℝ, +, •, <〉), various models of arithmetic (e.g., 〈ℕ, +, ·〉 or 〈ℕ, +〉), and other structures such as Boolean algebras or random graphs.
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Prof. Leonid Libkin
- Springer Berlin Heidelberg
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