Objective
The proposed research shall advance our knowledge in the field of set theory, a subfield of mathematical logic. Mildenberger proposes to work together with Shelah on some combinatorial questions in an area where independence of the axioms of mathematics, i.e. the Zermelo Fraenkel axiom system with together with the axiom of choice, short ZFC, is very likely. Therefore the main part of the proposed work is to develop forcing techniques. Combinatorial methods in the analysis of existing notions of forcing with respect to new properties would also be emphasised. In the proposed work, cardinal characteristics of the continuum often encapsulate important combinatorial features of the ZFC models in question. A cardinal characteristic of the continuum locates the smallest size of a set with a property that is usually not exhibited by any countable set and that is exhibited by at least one set of size of the continuum. However, sometimes a mathematical statement is derived from some delicate stratification of the set-theoretic universe that cannot (yet) be reduced to cardinal equations or inequalities. This can in particular be the case for set-theoretic universes that we intend to construct with not so conventional forcing constructions, such as non-linear forcing iterations and iterations with partial memory. We also propose to investigate forcings with oracle chain conditions. We want to advance these techniques further and develop new forcing constructions that will be useful for some longstanding open questions. The proposed research has applications to open problems in topology, algebra and in the combinatorics of the powerset of aleph_1. We propose to investigate the possible number of near-coherence classes of ultrafilters, some combinatorial properties of semifilters, and the connection between guessing principles and the existence of Souslin trees.
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 topology
- natural sciences mathematics pure mathematics algebra
- 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)
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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.
FP7-PEOPLE-2007-2-1-IEF
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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
91904 JERUSALEM
Israel
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.