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 natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsarithmetics Programme(s) 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) FP7-PEOPLE-2013-IEF - Marie-Curie Action: "Intra-European fellowships for career development" Call for proposal FP7-PEOPLE-2013-IEF See other projects for this call Funding Scheme MC-IEF - Intra-European Fellowships (IEF) Coordinator THE HEBREW UNIVERSITY OF JERUSALEM EU contribution € 192 464,40 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israel See on map Activity type Higher or Secondary Education Establishments Administrative Contact Hani Ben-Yehuda (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
