SDCE · On a question of Sacks and on the decidability of the two quantifier theory of the c.e. degrees

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Project objective

The proposed research involves investigation into two fundamental open problems in computability theory, both of which offer the potential for significant new progress. The first proposed area of investigation is a question due to Sacks as regards the existence of a degree invariant solution to Post's problem.The proposer has already developed new and exciting techniques with which he has been able to produce what is probably the strongest result on the positive side of the question. We propose to develop these techniques in order to give still stronger results, hopefully culminating in a full solution to the problem.The second proposed area of investigation is as regards the decidability of the two-quantifier theory of the c.e. degrees. Recent work in the area has suggested an approach to the relevant extensions of embeddings problem. The benefit of this approach is that there do seem to be approachable questions concerning extensions of embeddings, which involve finding solutions to some more particular questions concerning the structure of the c.e. degrees which are of considerable interest in themselves.The proposer will expand his knowledge of computability theory by gaining experience in the study of the Medvedev lattice and the enumeration reducibility. Through work with experts at the host institution in computational learning theory he will open up the possibility of future research in matters more directly related to computer science. Complimentary skills will be developed through a variety of means - in particular the proposer will attend courses in teaching methodology and will gain experience in the organization of conferences.The project is seen as a real opportunity for the proposer to expand his mathematical knowledge - both within his present field of expertise and in new areas - and to move towards a position of professional maturity and independence.

Original text from CORDIS.

Participants

• UNIVERSITÀ DEGLI STUDI DI SIENA · SIENACoordinatorItaly

Links

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