Fully Funded Studentship
University of East Anglia -Mathematics

School of Mathematics, Faculty of Science

Investigation of function spaces k^k, the generalised real numbers

Research Keywords:  Mathematics

Deadline: 1st April 2013. This studentship is available for a 1st October 2013 
start.

Supervisory Team: Primary: Professor Mirna Dzamonja (School of Mathematics) 
Secondary: Dr David Aspero (School of Mathematics)

The Project: The function space ww of the functions from the set of natural 
numbers to itself is the main object of research in mathematics: this is in 
fact the Baire space or the real numbers. It has been investigated from the 
point of view of descriptive and combinatorial set theory, topology and measure 
theory. We are interested in higher cardinal analogues of this space, for 
example the space w1w1 is the subject of investigation in [ii] and for k strong 
limit singular of cofinality w, the space kk is the subject of [i]. A striking 
difference exists between the two spaces mentioned here: the properties of the 
former one are very much independent of the axioms ZFC of set theory, while the 
properties of the latter one are computable in ZFC. This difference seeks to be 
explored: what happens when k is singular of uncountable cofinality, what about 
k successor of singular? These questions are in the heart of modern set theory 
and lie behind many other questions. To resolve them we need to use the modern 
techniques, and to develop new ones. This is the basis of this very ambitious 
Ph.D. project.

The ideal candidate will have a very strong background in mathematics and some 
experience in set theory.

Entry Requirements: A first class UK honours degree, or the equivalent 
qualifications gained outside the UK, in Mathematics.

Funding: This project is specifically funded for international students only. 
This funding includes full tuition fees and an annual stipend of £13,726. 
Funding is available for 3 years. Home/EU students are still welcome to apply 
provided they are able to secure their own source of funding.

Making Your Application: Please apply via the University?s online application 
system by clicking the APPLY button below. To discuss the application process 
or particular projects, please contact the: Admissions Office, email: 
pgr.enquiries.admiss@uea.ac.uk or telephone +44 (0)1603 591709.