Objective
The proposal is for a three year project focussing on a number of fundamental topics in the area of recursion theory and its applications to logic, mathematics and theoretical computer science.
In the area of recursive model theory, emphasis is on research involving a productive combination of techniques from computability theory and the theory of models. The main objective here will be to make significant progress with fundamental questions concerning the complexity of relations in recursive models for very basic classes of theories, to attempt solutions to some long-standing problems concerning minimal enumerations of classes of computably enumerable sets, and to investigate the relationship between naturally arising notions from recursive model theory and the Turing fine structure theory for the noncomputable universe.
Particular results sought here include:
To find the algebraic conditions for autostable models and models with finite and infinite algorithmic dimension in relative recursion representations; To prove differences between the classes of Rogers structures on computable enumerations of r.e. sets, recursive models and computable enumerations; The investigation of the relationship between the semi-lattices for reducibilities on different classes of subsets on N and the Rogers structures of computable enumerations; And the investigation of the lattice-theoretic properties of Rogers structures for different classes of constructive elements.
The second main area of research is concerned with the theory of Turing definability, and research objectives would involve work on three important groups of basic questions concerning definability, elementary equivalence and structure theory. Major research aims include:
To prove the definability of relations 'recursively enumerable" and 'recursively enumerable in" in degree structures of n- r.e. degrees for n>1; To prove the definability of omega-r.e. degrees in the upper semi-lattice of degrees of unsolvability (resulting in a definition of the d-r.e. degrees in the Turing degrees); And the study of interrelations between the hierarchies of REA- and n-r.e. degrees.
The final area of research is potentially a particularly fruitful one, concerning computability relative to partial information, using nondeterministic algorithms, formalised via the fundamental notion of enumeration reducibility (or e-reducibility). A basic objective of the research would be to improve understanding of the relationship between deterministic Turing reducibility and the structures deriving from enumeration reducibility. Anticipated results include:
Characterisation of the initial segments of the enumeration degrees;Relating rigidity of the e-degrees to that of the Turing degrees via automorphism bases; Proving the definability of the class of Turing degrees in the structure of the enumeration degrees; Characterisation of the local theory of the e-degrees; And characterising the automorphisms of the local structure of the e-degrees and proving the definability of this local structure in that of the Turing degrees.
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.
This project has not yet been classified with EuroSciVoc.
Be the first one to suggest relevant scientific fields and help us improve our classification service
You need to log in or register to use this function
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.
Data not available
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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.
Data not available
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.