| Unit name | Axiomatic Set Theory |
|---|---|
| Unit code | MATHM1300 |
| 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 | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
A natural heirarchy of sets, the constructible sets, first defined by Godel, is obtained by a transfinite recursion through all the ordinal numbers. The heirarchy has a very smooth character, and the uniformity of its presentation enables one to see that various questions that had been found to be unanswerable in Godel's day, have solutions in the resulting model of Zermelo-Fraenkel set theory, such as the Axiom of Choice (AC) and the Continuum Hypothesis (CH). It is now known that the AC and CH are neither provable nor disprovable from the other axioms. The universe of constructible sets is a model of these statements and hence we see that they are at least non-contradictory.
