Objective Topic: The topic of the project is set theory, in particular forcing theory. We will investigate internal consistency and the outer model program. Who and where: The researcher is Jakob Kellner, currently Marie Curie EIF fellow at the Hebrew University in Jerusalem, Israel (scientist in charge: Saharon Shelah). The project will be carried out at the Kurt Gödel Research Center for Mathematical Logic at the University of Vienna (KGRC). Scientist is charge will be Sy David Friedman, the head of the KGRC. How: Jakob Kellner has a contract as Assistent (non-tenure track assistant professor) from September 2008 (the end of the current EIF project) until November 2013. The ERG money will mainly contribute to travel and collaboration costs during the first 3 years. What: Set theory offers very general and powerful methods to prove mathematical theorems. In some cases, these methods actually prove that certain mathematical sentences are undecidable. Such proofs typically use the method of forcing. The first example of this kind (Cohen) was the continuum hypothesis (CH). Global questions (such as the generalized continuum hypothesis, GCH) require class forcing (Easton). Another important notion for consistency is the theory of inner models. The first example was Gödel's constructible universe L, satisfying CH and the Axiom of Choice (AC). Often, the consistency strength of a statement is strongert than ZFC. Then large cardinals (LC) are used to gauge the consistency strength, and the incompleteness phenomenon can be capured by consistency results of the form: Assuming LC, a certain sentence is consistent. For example (Solovay), assuming an inaccessible cardinal, consistently every definable set of reals is Lesbegue measurable. One topic is internal consistency: A sentence is internally consistent (ICon), if it holds in an inner model. An internal consistency theorem has the form: ICon(LC) implies Con(T). Fields of science natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logic Keywords Forcing Mathematical Logic Set theory 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) PEOPLE-2007-2-2.ERG - Marie Curie Action: "European Reintegration Grants" Call for proposal FP7-PEOPLE-2007-2-2-ERG See other projects for this call Funding Scheme MC-ERG - European Re-integration Grants (ERG) Coordinator UNIVERSITAT WIEN EU contribution € 45 000,00 Address UNIVERSITATSRING 1 1010 Wien Austria See on map Region Ostösterreich Wien Wien Activity type Higher or Secondary Education Establishments Administrative Contact Sy David Friedman (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
