Large Properties at Small Cardinals

Objective

Large cardinals are deeply used in set theory as many problems that are independent from the classical theory ZFC can be solved under the assumption that large cardinals exist. One of the most rich and fruitful research areas in contemporary set theory is the study of those properties of large cardinals that can hold even at small cardinals. Two properties of that kind are particularly interesting, the strong tree property and the super tree property. These properties provide a simple combinatorial characterisations of very strong large cardinal notions, namely strongly compact cardinals and supercompact cardinals. Although the strong and super tree property are associated with such strong large cardinals, they can be satisfied even by small cardinals such as aleph_2. The project focuses on some potential applications of such properties at small cardinals. Two conjectures are stated, the first one implies that the strong tree property has strong consequences in the arithmetic of infinite cardinals, namely we conjecture that the strong tree property at aleph_2 implies the singular cardinal hypothesis. The second conjecture concerns the study of infinite almost abelian groups, more precisely we ask whether the super tree property at a small cardinal kappa implies that every almost free abelian group of size kappa is free. The project is concerned more generally with developing combinatorial characterisations of all large cardinal notions and it proposed a systematic analysis of the combinatorial principles associated with large cardinals.

Fields of science (EuroSciVoc)

CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.

• natural sciences mathematics pure mathematics discrete mathematics mathematical logic
• natural sciences mathematics pure mathematics arithmetics

Programme(s)

Multi-annual funding programmes that define the EU’s priorities for research and innovation.

• FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)

Topic(s)

Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.

• FP7-PEOPLE-2013-IEF - Marie-Curie Action: "Intra-European fellowships for career development"

Call for proposal

Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.

FP7-PEOPLE-2013-IEF
See other projects for this call

Funding Scheme

Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.

MC-IEF - Intra-European Fellowships (IEF)

Coordinator