Language, Logic and Computations

  • Pavel Pudlák
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Turing Machine Recursive Function Computable Function Atomic Formula Intuitionistic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Pavel Pudlák
    • 1
  1. 1.ASCRPragueCzech Republic

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