Mathematical Logic

Syllabus:

Classical propositional calculus (PC): Syntax. Valuations and truth tables, Truth functions, Logical equivalence relation. Semantic consequence and satisfiability. Compactness theorem with application. Adequacy of connectives. Normal forms.

Axiomatic approach to PC: soundness, consistency, completeness. Other proof techniques: Sequent calculus, Computer assisted formal proofs: Tableaux. Decidability of PC,

Boolean algebras: Order relations. Boolean algebras as partially ordered sets. Atoms, Homomorphism, sub-algebra. Filters. Stone's representation (sketch). Completeness of PC with respect to the class of all Boolean algebras.

Classical first order logic (FOL) and first order theories, Syntax. Satisfaction, truth, validity in FOL. Axiomatic approach, soundness. Computer assisted formal proofs: Tableaux. Consistency of FOL and completeness (sketch). Equality. Examples of first order theories with equality.

References:

1. R. Cori and D. Lascar: Mathematical Logic, Oxford, 2001.
   

2. I. Chiswell and W. Hodges: Mathematical Logic. Oxford, 2007.
   

3. J. Kelly: The Essence of Logic, Pearson, 2011.
   

4. A. Margaris, First Order Mathematical Logic, Dover, 1990.