Iterated forcing and high forcing axioms (ASPERO_U17SCI)

University of East Anglia - School of Mathematics

Start Date: October 2017

No. of positions available: 1

Supervisor: Dr David Aspero

Project description: Forcing axioms are principles occurring naturally in set theory. These principles assert that some initial segment of the universe is saturated, in some well-defined sense, relative to some large number of generic extensions. Models of these principles are naturally produced by suitable iterated forcing extensions. Due to technical reasons, most classical strong forcing axioms pertain the initial segment of the universe known as H(\omega_2). The iteration techniques for producing models of strong forcing axioms at the level of H(\omega_3) or higher up are new or yet to be developed. This PhD project aims at developing these techniques and studying the combinatorial consequences of this type of axioms.

Interviews will take place between 16 January and 24 February 2017.

Person specification: Mathematics degree (2:1 or higher) at Masters Level or equivalent

Funding notes: This PhD project is in a Faculty of Science competition for funded studentships. These studentships are funded for 3 years and comprise home/EU fees, an annual stipend of £14,296 and £1000 per annum to support research training. Overseas applicants may apply but they are required to fund the difference between home/EU and overseas tuition fees (in 2016/17 the difference is £12,879 for the Schools of CHE & PHA, and £9,679 for CMP & MTH but fees are subject to an annual increase)

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