Naive and Axiomatic Set Theory (U03436)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-4-NAS

Course for final year students in Honours programmes in Mathematics.

1. Development in naive set theory of Cantor's basic results on cardinals and ordinals.

2. The Schroder-Bernstein Theorem and cardinal arithmetic, including exponentiation.

3. Ordinal number theory, the Axiom of Choice and Zorn's Lemma.

4. The formal axiomatic ZFC set theory and the role of the axioms in mathematics, including Power set, Choice, and Replacement.

5. Non-standard models in set theory. Inaccessible cardinals.

6. Independence results.

7. Godel's model of constructible sets, with reference to Choice and Continuum Hypothesis.

Entry Requirements

none

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Not being delivered

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Wednesday	14:00	14:50	KB

Summary of Intended Learning Outcomes

1. To understand how to set up the language of set theory.
2. To understand and use the concepts of transfinite cardinal and ordinal arithmetic.
3. To understand an axiom system for set theory.