| Unit name | Logic 4 |
|---|---|
| Unit code | MATHM6207 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
| Unit director | Professor. Welch |
| Open unit status | Not open |
| Pre-requisites |
Level 4/C Pure Mathematics units (MATH11006, MATH11511 & MATH11521) |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
We use mathematical techniques to analyse formal propositional and predicate languages, together with the structures they can describe. We study the notions of satisfiability, validity and logical consequence. We prove the completeness theorem (that the set of sentences provable from a set of axioms is precisely the same set of sentences as those that are true in all structures in which the axioms are true. We discuss the First Incompleteness Theorem of Godel, that not all true statements of arithmetic are provable from any effectively given set of axioms for number theory. For level 7/M we shall look carefully at the details of both this theorem and Godel's Second Incompleteness Theorem, that sufficiently strong systems cannot prove their own consistency.
