Objective
"This project aims at applying the most recent results and techniques of topos theory to predicative Mathematics. The theoretical and applicative objectives it addresses, can be achieved by using in a substantial new way Grothendieck toposes and their theory, a possibility arisen in 2009 after the discoveries of O. Caramello.
Predicative Mathematics is the branch of pure Mathematics that considers (well-founded) construction as the unique paradigm for its development, at any level of granularity: for this reason, it has a natural interpretation as the ‘Mathematics of the computable’ since, to every theorem or definition it is possible to associate a construction which can be thought of as an abstract algorithm.
This project wants to characterize predicative theories in explicit topos-theoretic terms, i.e. it requires to find a formal description in the language of Grothendieck toposes to decide whether a mathematical theory is predicative, and, in the positive case, to formally associate to every theorem and definition their natural constructions. The aim is to transfer results proved in impredicative settings into the predicative world, by using the topos-theoretic description of an impredicative theory as a “bridge” toward a suitable predicative presentation.
In the opposite direction, the project wants to develop a method to synthesize algorithms in impredicative frames by importing the intrinsic computational meaning of a predicative presentation.
So, ultimately, this project wants to address the fundamental question whether every mathematical theory admits a predicative presentation and, if not, to what extent one can ‘approximate’ impredicative theories via predicative ones."
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.
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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-2010-IEF
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
LS2 9JT Leeds
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.