### MA6190 Mathematical Logic (modified)

#### Course Details

Formal proofs, resolution, Axiom systems, strong completeness and compactness of propositional logic.

First order with equality: First order structures in mathematics, Propositional reduction, completeness and compactness.Variants of Lowenheim-Skolem theorem. Some complete axiom systems. Isomorphisms and equivalence of structures. Expressive and distinguishing power of First order logics. EF games and 0-1 law. Proof sketch of Incompleteness theorems. Undecidability.

#### Course References:

Text Books:

1. A. Singh, Logics for Computer Science, PHI Learning. 2003

2. Lecture notes by Madhavan Mukund and S P Suresh (https://www.cmi.ac.in/~madhavan/papers/pdf/logic-aug2011.pdf)

Reference Books:

1. A Friendly Introduction to Mathematical Logic - Christopher C. Leary, Lars Kristiansen - Milne Library 2nd edition 2015.

2. A course in mathematical logic - Yu I Manin – Springer. 1977

3. S. Bilaniuk, A Problem Course in Mathematical Logic, GNU Free Documentation, http://euclid.trentu.ca/math/sb/pcml/, 2003.

4. Leonid Libkin, Elements of Finite Model Theory, Springer, 2004. (https://homepages.inf.ed.ac.uk/libkin/fmt/fmt.pdf)