Fully Funded Studentship Pure and Applied Set Theory Faculty of Science University of East Anglia -School of Mathematics Research Keywords: Mathematics Deadline: 28 February 2013. Supervisory Team: Primary: Prof M Dzamonja The Project: Set theory is part of the foundation of mathematics. On the one hand, it belongs to mathematical foundations and logic, and on the other hand it belongs firmly to mathematics. Set theoretic methods have been used to answer questions in topology, measure theory, Boolean algebras, Banach spaces, group theory and other parts of mathematics. We are working on a number of questions involving methods from combinatorial set theory, such as pcf theory and forcing, and to a lesser extent, descriptive set theory. Some concrete problems proposed are applications of new methods in forcing axioms, including forcing object on cardinal aleph_2 and above. This project is also open to applicants (Home, EU or Overseas) who have their own funding. Self-funded applicants may apply to study on a part-time basis. References: Set Theory, third millennium edition, T. Jech Entry Requirements: The standard minimum entry requirement is a 1st in Mathematics Funding: Funding will cover home/EU fees only. Overseas students will be required to pay the difference between home/EU and overseas fees. Making Your Application: Please apply via the University's online application system which can be accessed by the Apply link 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. ================================== 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.