Course pages 2011–12
This module aims to provide the basic mathematical logic which will be assumed in later courses.
Based on Enderton A mathematical introduction to logic
- Propositional Calculus: truth-functional models, a deductive calculus and a proof of soundness and completeness.
- First-Order Predicate logic: Tarskian truth and models, a deductive calculus and a proof of soundness and completeness.
- Compactness and Loewenheim-Skolem theorems.
- First-order theories and their models: some examples with indications (and in some cases proofs) of which theories are complete/incomplete: Dense linear orders, Natural numbers with successor, Pressburger arithmetic, Peano arithmetic, Real-closed fields.
[There are plans to revise this syllabus for 2011-12; these replace some existing material with lectures on Intuitionistic Logic and the Curry-Howard Correspondence.]
On completion of this module, students should:
- have a good understanding of propositional and first order logic, their proof systems and models.
Based on a take-home test exam, possibly supplemented by weekly handout exercises.
Enderton, H.B. (2001). A mathematical introduction to logic. Academic Press (2nd ed.).