Objective
The proposed project is devoted to inner model theory, an area of set theory, and its applications in infinitary combinatorics and descriptive set theory. The main goal of inner model theory is constructing canonical models, or extender models, for axioms postulating the existence of 'higher level infinity', the so-called large cardinal axioms.
Extender models are used (a) to establish consistency strengths for mathematical statements that cannot be decided by means of the standard axioms of set theory, the Zermelo-Fraenkel axioms, and (b) to extract information about sets that depends on large cardinals alone.
The project is divided into 4 parts:
The 1. part focuses on the analysis of the internal structure of extender models and studying combinatorial principles in these models using purely fine structural methods. The goal here is to generalize Jensen and analysis of Goedel's constructible universe to the broader context of extender models.
The 2. part is devoted to applications of the existing inner model theory in improving the known lower bounds for consistency strengths of various set-theoretic statements, such as the failure of Jensen and principle Diamond at Mahlo cardinals under GCH, failure of Jensen and principle square at singular cardinals, or bounded Martin Maximum.
The 3. part concentrates on connections between inner model theory and descriptive set theory; the objectives here include
- establishing optimal hypotheses for correctness results at higher level of projective hierarchy and
- finding inner model characterizations of objects known from classical descriptive set theory.
The 4. part is devoted to constructions of inner models, and the emphasis is on studying the complexities of iteration strategies for countable extender models and determining limitations of currently known methods for obtaining iterability.
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.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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.
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
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2004-MOBILITY-5
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.
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
BERLIN
Germany
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.