MA6190 Mathematical Logic


Course Details

Basics of First order logic: Syntax of FL, formal semantics of FL, satisfiability, validity, equivalence, equality sentences, prenex form, Skolemization, Herbrand interpretation, Skolem-Lowenheim theorem.
Proofs in FL: A Hilbert style axiom system, soundness and completeness, compactness, analytic tableax, mathematical theories, axiomatization of arithmetic.
Issues about FL: Undecidability, definability, expressibility, negation incompleteness, unprovability of consistency of arithmatic.

Course References:

Texts books:
1. A. Singh and C. Goswami, Fundamentals of Logic, ICPR, New Delhi, 1998.
2. S. Bilaniuk, A Problem Course in Mathematical Logic, GNU Free Documentation, http://euclid.trentu.ca/math/sb/pcml/, 2003.
References:
1. A. Singh, Logics for Computer Science, PHI Learning, New Delhi, 2003.
2. R.M. Smullyan, A Beginner's guide to Mathematical Logic, Dover Publications, Inc. New York, 2014.
3. H.B. Enderton, A Mathematical Introduction to Logic, 2nd Ed., Harcourt/Academic Press, New York, 2001.
4. Yu.I. Manin, A Course in Mathematical Logic for Mathematicians, 2nd Ed., Springer-Verlag, New York, 2008.