Course Archives Theoretical Statistics and Mathematics Unit

Course: Mathematical Logic Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus: i) Syntax of First-Order Logic: First Order Languages, Terms and Formulas of a First Order language, First Order Theories. ii) Semantics of First-Order Languages: Structures of First-Order Languages, Truth in a Structure, Model of a Theory. iii) Propositional Logic: Tautologies and Theorems of propositional Logic, Tautology Theorem iv) Proof in First Order Logic, Metatheorems of a first order theory, e.g., theorems on constants, equivalence theorem, deduction and variant theorems etc., Consistency and Completeness, Lindenbaum Theorem. v) Henkin Extension, Completeness theorem, Extensions by definition of first order theories, Interpretation theorem. vi) Model Theory: Embeddings and Isomorphisms, Lowenheim-Skolem Theorem, Compactness theorem, Categoricity, Complete Theories. vii) Recursive functions, Arithmatization of first order theories, Decidable Theory, Representability, Godel’s first Incompleteness theorem. Suggested Texts : (a) S. M. Srivastava, A Course on Mathematical Logic, Springer (2013). (b) J. R. Shoenfield, Mathematical logic, Addison-Wesley (1967). Top of the page Past Exams

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[ Semester Schedule ][ SMU ] [Indian Statistical Institute]