# MA3H3 - Set Theory

**Module code:**MA3H3**Module name:**Set Theory**Department:**Mathematics Institute**Credit:**15

Content and teaching | Assessment | Availability

## Module content and teaching

###### Principal aims

The module will commence with a brief review of naive set theory. Unrestricted set formation leads to various paradoxes (Russell, Cantor, Burali-Forti), thereby motivating axiomatic set theory. The Zermelo-Fraenkel system will be introduced, with attention to the precise formulation of axioms and axiom schemata, the role played by proper classes, and the cumulative hierarchy picture of the set theoretical universe. Transfinite induction and recursion, cardinal and ordinal numbers, and the real number system will all be developed within this framework. The Axiom of Choice, and various equivalents and consequences, will be discussed; various other principles also known to be independent of Zermelo-Fraenkel set theory, such as the Continuum Hypothesis and the existence of Inaccessible Cardinals, will be touched on.

###### Departmental link

http://go.warwick.ac.uk/MA3H3/

###### Other essential notes

Prerequisites: MA132 Foundations or PH126 Starting Formal Logic. Some exposure to at least one of MA222 Metric Spaces, MA359 Measure Theory or PH210 Symbolic Logic is also recommended.

## Module assessment

Assessment group | Assessment name | Percentage |
---|---|---|

15 CATS (Module code: MA3H3-15) | ||

B (Examination only) | 3 hour examination (April) | 100% |

## Module availability

This module is available on the following courses:

###### Core

- Undergraduate Mathematics and Philosophy (GV17) - Year 3
- Undergraduate Mathematics and Philosophy with Intercalated Year (GV18) - Year 4
- Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 3

###### Optional Core

- Undergraduate Mathematics and Philosophy (GV17) - Year 3
- Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 4

###### Optional

- Undergraduate Mathematics (BSc) (G100) - Year 3
- Undergraduate Mathematics with Intercalated Year (G101) - Year 4
- Undergraduate Mathematics (MMath) (G103) - Year 3
- Undergraduate Mathematics (MMath) (G103) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 3
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 4
- Undergraduate Master of Mathematics (with Intercalated Year) (G105) - Year 5
- Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 3
- Undergraduate Mathematics (MMath) with Study in Europe (G106) - Year 4
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 3
- Undergraduate Mathematics and Statistics (BSc MMathStat) (G1G3) - Year 4
- Postgraduate Taught Mathematics (G1P0) - Year 1
- Postgraduate Taught Mathematics (G1P0) - Year 2
- Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 1
- Postgraduate Taught Mathematics (Diploma plus MSc) (G1PC) - Year 2
- Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 1
- Postgraduate Taught Interdisciplinary Mathematics (Diploma plus MSc) (G1PD) - Year 2
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G300) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30A) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30B) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30C) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (G30D) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30E) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30F) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30G) - Year 5
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 3
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 4
- Undergraduate Master of Mathematics,Operational Research,Statistics and Economics (with Intercalated (G30H) - Year 5
- Undergraduate Discrete Mathematics (G4G1) - Year 3
- Undergraduate Discrete Mathematics with Intercalated Year (G4G2) - Year 4
- Undergraduate Discrete Mathematics (G4G3) - Year 3
- Undergraduate Mathematics and Physics (BSc) (GF13) - Year 3
- Undergraduate Mathematics and Physics (with Intercalated Year) (GF14) - Year 4
- Undergraduate Mathematics and Statistics (BSc) (GG14) - Year 3
- Undergraduate Mathematics and Statistics (with Intercalated Year) (GG17) - Year 4
- Undergraduate Mathematics and Economics (GL11) - Year 3
- Undergraduate Mathematics and Philosophy with Specialism in Logic and Foundations (GV19) - Year 3
- Undergraduate Mathematics,Operational Research,Statistics and Economics (Y602) - Year 3
- Undergraduate Mathematics,Operational Research,Statistics,Economics (with Intercalated Year) (Y603) - Year 4