Mathematical Logic

Katalin Bimbo is Associate Professor at University of Alberta. She has published three other well-received books on logic including Proof Theory: Sequent Calculi and Related Formalisms (CRC Press, 2014). She received a Faculty of Arts Reasearch Excllence Awared in 2012.

Chapter 1. Language and interpretation of first-order logic


Chapter 2. Proof systems: sequent calculus, tableaux, axiomatic calculus


Chapter 3. Propositional logic (as a restriction of rst-order logic), truth tables, disjunctive and conjunctive normal forms, prenex normal forms


Chapter 4. Resolution calculus and its applications; equivalence of proof calculi


Chapter 5. Core metatheorems I: Soundness and completeness proofs (including separate proofs for propositional logic and di erent constructions for the quanti cational case)


Chapter 6. Core metatheorems II: Compactness, upward and downward L•owenheim{Skolem theorems, Lindstr •om's theorem


Chapter 7. Core metatheorems III: Craig's interpolation theorem, Robinson's consistency theorem, Beth's de nability theorem


Chapter 8. Core metatheorems IV: Undecidability, the impact of the metatheorems


Chapter 9. Expressibility and de nability (variations on the set of logical connectives and the set of logical operators; choosing and modifying the non-logical vocabulary)


Chapter 10. Algebraizations (Boolean algebra for propositional logic, cylindric algebra and polyadic algebra for rst-order logic)


Chapter 11. Mathematical theories within first-order logic (varieties: semi-groups, groups, etc.; ordered structures; arithmetic; set theory)


Chapter 12. Decidability (propositional logic, classes of quanti cational formulas speci ed by quanti er prex, by shape of formulas)


Chapter 13. Complexity (satis ability problem, validity problem)


Chapter 14. Categorial view (category of proofs, quanti ers as adjoint functors)