Titlebook: A Course on Mathematical Logic; S. M. Srivastava Textbook 20081st edition Springer-Verlag New York 2008 computability theory.mathematical

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Textbook 20081st editionthematics and computer science. Any mathematician who is interested in knowing what logic is concerned with and who would like to learn G?del’s incompleteness theorems should find this book particularly convenient. The treatment is thoroughly mathematical, and the entire subject has been approached

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A Course on Mathematical Logic978-0-387-76277-7Series ISSN 0172-5939 Series E-ISSN 2191-6675

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https://doi.org/10.1057/9781137446770ch as groups, rings, fields, algebraically closed fields, etc., with the aim to develop tools to examine their consistency, completeness, and other similar questions concerning the foundation of these theories. In this chapter we take the first step toward logic and precisely define the notion of a firstorder theory.

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Thibauld Moulaert,Suzanne GaronIn the previous chapter, we introduced the notion of proof in propositional logic. In this chapter we shall define proof in a first-order theory and prove several metatheorems in first-order logic.

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Vera Roos,Puleng Segalo,Ngenisiwe NtombelaIn this chapter we shall study recursive functions.We shall also introduce techniques to show how a general decision problem can be converted into showing whether a partcular function is recursive.

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Vera Roos,Anél du Plessis,Jaco HoffmanThis chapter gives the most important landmarks of mathematical logic— the incompleteness theorems of G?del.We still have to do some work, which we do in the first section. As a side output, in Section 3, we initiate the study of recursion theory.

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