Objective
This proposal is in mathematical logic. It aims to study interactions between set theory and computability. More specifically, we want to apply techniques from inner model theory to computability and randomness.
The development of modern set theory began with Paul Cohen's solution of Hilbert's first problem in 1964. Since then, set theory has been used to solve important problems in various areas of mathematics. Descriptive set theory studies definable sets of reals, for instance Borel and analytic sets, and computability studies computable functions and its higher analogues.
We propose to develop applications of inner model theory in computability. Inner model theory is a major field of set theory which was pursued for instance by Ronald Jensen (recipient of the AMS Steel prize 2003 and Hausdorff medal 2015) and Hugh Woodin (recipient of the Hausdorff medal 2013). A major aim of this field is to determine the logical strength of theories. Recently, several new approaches for constructions of inner models have been studied, for example via strong logics by Menachem Magidor and Jouko Väänänen. We propose to follow this line of research and to study models constructed via ideas from infinite computation related to work of Joel David Hamkins and Philip Welch.
We further propose to apply inner model theory and descriptive set theory to study random sequences. Algorithmic randomness is a central field in computability with connections to theoretical computer science, that has been studied intensively, for instance by Ted Slaman and Andre Nies. We aim to solve problems in the higher generalizations of algorithmic randomness.
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 computer and information sciences computational science
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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.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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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.
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.
MSCA-IF-EF-ST - Standard EF
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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.
(opens in new window) H2020-MSCA-IF-2017
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
BS8 1QU BRISTOL
United Kingdom
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.