Course pages 2011–12

# Introductory Logic

**Principal lecturer:** Prof Alan Mycroft**Taken by:** MPhil ACS, Part III**Code:** R07**Hours:** 8**Prerequisites:** Some mathematical maturity

## Aims

This module aims to provide the basic mathematical logic which will be assumed in later courses.

## Syllabus

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.]

## Objectives

On completion of this module, students should:

- have a good understanding of propositional and first order logic, their proof systems and models.

## Coursework

See below.

## Practical work

None.

## Assessment

Based on a take-home test exam, possibly supplemented by weekly handout exercises.

## Recommended reading

Enderton, H.B. (2001). *A mathematical introduction to logic.*
Academic Press (2nd ed.).