Objective
One of the principal threads in Mathematical Logic is to give a mathematical analysis of the notion of definability. Of particular interest is the relative definability of reals. Based on the fineness of ingredients that come into a particular definability notion, we obtain a whole spectrum of relative definability: effective translation (many-one reducibility), computation (Turing reducibility), existential definability (enumeration reducibility), number theoretic definability (arithmetic reducibility), and definability by the Borel operations (hyperarithmetic reducibility). We propose to study the spectrum of relative definability between subsets of the natural numbers. At the two endpoints, many-one and hyperarithmetic, we do have complete accounts and those accounts are completely different. We have only partial understanding of the spectrum between these two extremes and many important open questions. The main objective of this project is to study the to understand where in the spectrum moving from top to bottom the difference occurs. A special focus in this project will be the pair of the Turing and Enumeration degrees which is expected to hold the key for understanding this central question. The proposed project is inter-sectoral in its essence, as it examines the connection between structures that arise from Computability Theory with the structure of Second Order Arithmetic.The methodology used for these investigations place them at the intersecting point between the Computability Theory, Set Theory and Descriptive Set Theory.
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 mathematical analysis
- natural sciences mathematics pure mathematics arithmetics
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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.
FP7-PEOPLE-2011-IOF
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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
1504 Sofia
Bulgaria
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.