Language, Logic and Computations

In this chapter we present the main concepts of mathematical logic. We describe the formal language used in mathematical logic, which is a formalization of the language used in mathematics. We explain how this language is applied to mathematical structures, which are called models in this context. We show how proofs, the main product of mathematical research, are formalized. We also present the main concepts of the theory of computations. Finally, we consider an important formal system, the λ-calculus, which can be used to formalize logical reasoning and computations at the same time.

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