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PH436 Half Unit

Set Theory

**This information is for the 2023/24 session.**

**Teacher responsible**

Prof Miklos Redei and Dr Wesley Wrigley

**Availability**

This course is available on the MSc in Economics and Philosophy, MSc in Philosophy of Science and MSc in Philosophy of the Social Sciences. This course is available as an outside option to students on other programmes where regulations permit.

**Pre-requisites**

MSc students taking this course should already have taken a year-long introductory course in logic in a philosophy department, or a mathematical course that covers the basics of set theory or logic.

**Course content**

The aim of the course is to make students of philosophy familiar with the elements of naive set theory. Two types of concepts and theorems are covered: (i) the ones needed to understand the basic notions, constructions and mode of thinking in modern mathematical logic (ii) those that have philosophical-conceptual significance in themselves (elementary theory of ordinals and cardinals, transfinite induction, Axiom of Choice, its equivalents and their non-constructive character, Continuum Hypothesis, set theoretical paradoxes such as Russell paradox). The emphasis is on the conceptual-structural elements rather than on technical-computational details. Not all theorems that are stated and discussed are proven and not all proofs are complete. Students taking this course should tolerate abstract mathematics well but it is not assumed that they know higher mathematics (such as linear algebra or calculus).

**Teaching**

15 hours of lectures and 15 hours of seminars in the AT.

10 x 1.5 hours of lectures and 10 x 1.5 hours of seminars in the Autumn Term.

**Formative coursework**

Students are required to submit solutions to two problem-sets, and write one essay (word limit 1500 words) on a topic selected from a list or proposed by the student and approved by the instructor in the AT.

**Indicative reading**

- Cameron, Peter J. 1999. Sets, Logic and Categories. Springer undergraduate mathematics series. London, Berlin, Heidelberg: Springer.
- Halmos, Paul: Naive Set Theory (Springer reprint 2011)

**Assessment**

Exam (100%, duration: 2 hours) in the January exam period.

The exam questions are chosen from a list of questions that are made available at the beginning of the academic year ("seen exam").

** Key facts **

Department: Philosophy, Logic and Scientific Method

Total students 2022/23: Unavailable

Average class size 2022/23: Unavailable

Controlled access 2022/23: No

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

- Self-management
- Problem solving
- Application of numeracy skills
- Specialist skills