Objective
"This proposed research is in mathematical logic and foundations of mathematics, more specifically in set theory. It is motivated by the interplay between regularity properties and definability for subsets of real numbers. By ""regularity properties"" we are referring to certain desirable properties of sets, and by ""definability"" to the logical description of such sets, in the sense of Descriptive Set Theory.
The study of such questions goes back to classical issues in topology, analysis and related fields of mathematics, raised by the great pioneers of abstract mathematics of the late 19th and early 20th century, such as Georg Cantor, Emile Borel, Henri Lebesgue and others. These mathematicians were faced with seemingly insurmountable challenges which could only be resolved later with the advent of logical and meta-mathematical methods, developed by Kurt Gödel in 1938 and by Paul Cohen in 1964.
Since that time, the study of Regularity Properties has continued to hold a central position in the foundations of mathematics. Many mathematicians and logicians of high status and prestige have contributed to this area, among them W. Hugh Woodin (winner of the Hausdorff Medal 2013), Stevo Todorčević (winner of the CRM-Fields-PIMS prize 2012) and Saharon Shelah (winner of numerous awards, among them the Erdös Prize 1977 and the Karp Prize 1983).
We propose to contribute to this line of research in a number of interrelated directions, such as: studying new regularity properties (relevant to other fields of mathematics), developing abstract frameworks for such properties, studying higher complexity classes, and generalising results to spaces other than the classical real numbers. Several technical results involving the method of ""forcing"" needed to construct models of set theory, will also be worked out along the way."
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics topology
- natural sciences mathematics pure mathematics discrete mathematics combinatorics
You need to log in or register to use this function
We are sorry... an unexpected error occurred during execution.
You need to be authenticated. Your session might have expired.
Thank you for your feedback. You will soon receive an email to confirm the submission. If you have selected to be notified about the reporting status, you will also be contacted when the reporting status will change.
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.
-
H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
See all projects funded under this programme -
H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
See all projects funded under this programme
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
See all projects funded under this funding scheme
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-2015
See all projects funded under this callCoordinator
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.
20148 Hamburg
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.