Details of Grant 

EPSRC Reference:	GR/S44334/01
Title:	Interactions between combinatorics of stationary sets, bounded forcing axioms and inner models of set theory
Principal Investigator:	Welch, Professor PD
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Bristol
Scheme:	Standard Research (Pre-FEC)
Starts:	06 October 2003	Ends:	05 December 2005	Value (£):	104,426
EPSRC Research Topic Classifications:	Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 10 Jun 2003 Mathematics Prioritisation Panel Science Deferred
Summary on Grant Application Form
The project is one of pure mathematics. We wish to establish connectionsbetween some rather recent developments in several adjoining areas in set theory. (A) the so-called Bounded Forcing Axioms - generalising Martin's Axiom; (B) the theory of projective stationary sets and their allied forcing notions; (C) notions of mutual stationarity and other forms of stationarity connected to sequences of sets.It has recently been realised that Bounded Forcing Axioms limit the range of of consistency results provable using forcing. We wish to demonstrate the strength of some of these axioms qua strong axioms of infinifty;we further wish to prove that the notions of mutual stationarity interact with the so-called inner models of ZF set theory, such as the Constructable Universe, L, of Godel with which he showed the consistancy of the Axiom of Choice, and Continuum Hypothesis, with ZF. The areas (A)-(C) have only recently been developed; we therefore consider the project timely, and wish to, in particular to examine their interaction wit each other more carefully so as to provide set theorists with aclearer picture of their relationship. If we acheive this then we have shown that certain of the Bounded Forcing Axioms are truly of the nature of strong axioms of infinity going beyond ZF.We have as proposed RA someone welplaced to do fundamental research on this project, being now an expert on such Bounded Forcing Axioms.
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Organisation Website:	http://www.bris.ac.uk