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 (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.
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.
- engineering and technology materials engineering amorphous solids amorphous semiconductors
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
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Keywords
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Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
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Topic(s)
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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.
Call for proposal
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP7-PEOPLE-2007-2-2-ERG
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Funding Scheme
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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.
Coordinator
1010 WIEN
Austria
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