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CLASSFORCING

"Class forcing, internal consistency and the outer model program."

Coordinatore	UNIVERSITAT WIEN Organization address address: UNIVERSITATSRING 1 city: WIEN postcode: 1010 contact info Titolo: Prof. Nome: Sy David Cognome: Friedman Email: send email Telefono: +43-1-4277 50501 Fax: +43-1-4277 9505
Nazionalità Coordinatore	Austria [AT]
Totale costo	45˙000 €
EC contributo	45˙000 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2007-2-2-ERG
Funding Scheme	MC-ERG
Anno di inizio	2008
Periodo (anno-mese-giorno)	2008-09-01 - 2011-08-31

Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITAT WIEN Organization address address: UNIVERSITATSRING 1 city: WIEN postcode: 1010 contact info Titolo: Prof. Nome: Sy David Cognome: Friedman Email: send email Telefono: +43-1-4277 50501 Fax: +43-1-4277 9505	AT (WIEN)	coordinator	0.00

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continuum scientist del icon eif forcing form mathematical strength charge model jakob kgrc inner prove first consistency hypothesis sentence theory certain ouml consistent assuming ch internal university kellner lc

Obiettivo del progetto (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).'

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