Participating teams and local coordinators:
Siena (A. Sorbi)
Siegen (D. Spreen)
Novosibirsk (S. Goncharov)
Almaty (S. Badaev)
Final Report (July1, 2001- July 31, 2004) (word file)
Papers and conferences originating from the project
Completeness and universality of arithmetical numberings , by S. Badaev, S. Goncharov and A. Sorbi (pdf), in Computability and Models: Perspectives East and West (S. B. Cooper and S. S. Goncharov, eds.), Kluwer New York, Boston, Dordrecht, London, Moscow Academic/Plenum Publishers, pp. 11-44, 2003
Algebraic properties of Rogers semilattices of arithmetical numberings, by S. Badaev, S. Goncharov, S. Podzorov and A. Sorbi (pdf), in Computability and Models: Perspectives East and West (S. B. Cooper and S. S. Goncharov, eds.), Kluwer New York, Boston, Dordrecht, London, Moscow Academic/Plenum Publishers, pp. 45-77, 2003
Isomorphism types and theories of Rogers semilattices of arithmetical numberings, by S. Badaev, S. Goncharov and A. Sorbi (pdf), in Computability and Models: Perspectives East and West (S. B. Cooper and S. S. Goncharov, eds.), Kluwer New York, Boston, Dordrecht, London, Moscow Academic/Plenum Publishers, pp. 79-91, 2003
On elementary theories of Rogers semilattices, by S. Badaev, S. Goncharov and A. Sorbi (pdf), to appear in Algebra and Logic
A note on partial numberings, by S. Badaev, D. Spreen (pdf), to appear inMathematical Logic Quarterly
Elementary properties of Rogers semilattices of arithmetical numberings, by S. Badaev, S. Goncharov and A. Sorbi (pdf), in Proceedings of the 7-th and 8-th Asian Logic Conferences, R. Downey, D. Ding, S.H. Tung , Y. H. Qiu , M. Yasugi eds; associated editor G. Wu, World Scientific, Singapore, pp. 1-10, 2003
Isomorphism types of Rogers semilattices for different levels of the arithmetical hierarchy, by S. Badaev, S. Goncharov and A. Sorbi (pdf), to be submitted to Algebra and Logic, Preprint N. 460 (July 2004) of the Department of Mathematics and Computer Science “Roberto Magari”, University of Siena.
Computable and arithmetical numberings, by S. Badaev, S. Goncharov, A. Sorbi, International Conference Mathematical Logic, Algebra and Set Theory dedicated to the 100-th anniversary of P.S. Novikov, Moscow, August 26-31, 2001 (invited) (conference)
Automorphism groups of computably enumerable predicates, by E. F. Combarro, ( pdf), Algebra and Logic, Vol. 41, No.5, pp. 285-294, (2002)
On the Ershov upper semilattices $\mathfrak{L}_E$, by A. Khisamiev, Siberian Mathematical Journal , Vol. 45, No. 1, pp. 212-228, (2004)
Initial segments in Rogers semilattices of $\Sigma^0_n$-computable numberings, by S. Yu. Podzorov, Algebra and Logic, v. 42, No. 2, pp. 211-225, (2003)
On positive computability in Ershov’s hierarchy, by J. T. Talasbaeva, Algebra and Logic, Vol. 42, No. 6, pp. 737-746, (2003)
On the problem of finite signature, by A. Khisamiev, Siberian Mathematical Journal , Vol. 44, No. 1, pp. 206-210, (2003)
On $\Sigma$-subsets of natural numbers, by A. Morozov, V.G. Puzarenko, Algebra and Logic, Vol. 43, No. 3, pp. 291-320, (2004)
Boolean algebras with finite computable families of automorphisms, by A. Morozov, B. Kasymkhanuly, Siberian Mathematical Journal , Vol. 45, No. 1, pp. 171-177, (2004)
Strong reducibilities of partial numberings, by D. Spreen, ( pdf), to appear in Archive for Mathematical Logic
The largest cartesian closed category of domains – considered constructively, by D. Spreen, ( pdf), to appear in Mathematical Structures in Computer Science
About the limitness of the greatest element of a Rogers semilattice, by S. Podzorov, ( pdf), to appear in Siberian Mathematical Journal
Classification of limit reducibilities, by V. P. Dobritsa, M. G. Leonov, , to appear in Siberian Mathematical Journal
On homeomorphisms of effective topological spaces, by A. Morozov, ( pdf), to appear in Siberian Mathematical Journal
On quasiresolvable models, by A. Khisamiev, ( pdf), to appear in Algebra and Logic
On $\Sigma$-subsets of natural numbers in hereditary finite admissible sets, by A. Khisamiev, ( pdf), to appear in Siberian Mathematical Journal
On possible types of time in generalized computability theory, by A. Morozov, K. F. Samokhvalov, Vychislitelnye systemy, Methodological aspects of cognitive processes, No. 170, pages. 45-51, Novosibirsk, 2002 [Russian]
On incomparable enumerators on natural numbers, by A. Morozov, to appear in Vychislitelnye systemy, [Russian]
$\omega$-computable numberings, by S. Bereznyuk, submitted to Vestnik Novosibirskogo Universiteta, [Russian]
Degrees of algebraic systems and $\Sigma$-definability, by A. Khisamiev, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, pp.61-76 (paper)
Spectrum of minimal numberings for the families of arithmetical sets, by S. Badaev, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, pp. 18-25 (paper)
Computable boolean algebras, by P. Alaev, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, pp. 11-12 (abstract)
On limit constructible models, by V. Dobritsa, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, pp. 30-31 (abstract)
Computability and autostability, by S. Goncharov, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, pp. 33 (abstract)
Spectrum of atomless elements ideal, by P. Semukhin, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, p. 50 (abstract)
On the effective continuity of effective multifunctions, by D. Spreen, (pdf), Proceedings of the Workshop Computability and models, Almaty, June 24-28, 2002, p. 53 (abstract)
Limit constructive models as a methodology to solve economical problems in neural networks, by V. P. Dobritsa, N.G. Khisamiev, Proceedings of Scientific and Practical Conference Current Problems, Trends and Perspectives in Government of Regional Social and Economics Systems, 6-7 November, 2002, Ust-Kamenogorsk (Kazakhstan), pp. 283-284.
Elementary Theories of Rogers Semilattices, by S. Badaev, International Workshop Computability and Logic, Heidelberg, June 23-27, 2003
On quasiresolvable structures, by A. Khisamiev, Logic Colloquium 2003, Finland, Helsinki, August 14-20, 2003 (abstract)
Computability in Topological Spaces, by S. Badaev, Proceedings of the International Conference Algebra and Analisys–2004 Dedicated to the 200th Anniversary of the Kazan State University, Kazan, Kazan Mathematical Society, Kazan, July 2-9, 2004, p. 16
Quasiresolvable periodic Abelian groups, by A. Khisamiev, Logic Colloquium 2004, Italy, Turin, July 25-31, 2004 (abstract)
Rogers semilattices of arithmetical numberings, by S. Podzorov, Logic Colloquium 2004, Italy, Turin, July 25-31, 2004 (abstract)
Global and local properties of Rogers semilattices of arithmetical numberings, by S. Badaev, Workshop Computability and Models, Novosibirsk, September 24-26, 2001 (conference)
Arithmetical numberings, by S. Badaev, (pdf), Workshop Computability and Models, Almaty, June 24-28, 2002, (conference)
Complete numberings, by S. Badaev, (pdf), Workshop Computability in Hierarchies and Topological Spaces, Siena, July 20-23, 2004, (conference)
Enumerations in the theory of computable models,
by S. Goncharov,
(pdf),
Workshop Computability in Hierarchies and Topological Spaces,
Partial Numberings,
by D. Spreen,
Workshop Computability in Hierarchies and Topological Spaces,
Siena, July 20-23, 2004, (conference) On some constructions in the theory of numberings,
by S.Badaev, S.Goncharov, A.Sorbi,
in preparation for the journal
Mathematical Notes, On the effective continuity of effective multifunctions,
by D. Spreen,
in preparation On decompositions of Rogers semilattices,
by S. Badaev , S.Lempp,
in preparation On completions of numberings,
by Z. Khisamiev,
in preparation for the journal
Algebra and Logic, Lattice of numberings generated by completions,
by Z. Khisamiev,
in preparation for the journal
Algebra and Logic, Positive numberings in effective
domains,
by A. Altaeva , S. Badaev,
in preparation for the journal
Algebra and Logic, On the local structure of Rogers semilattices
of $\Sigma^0_n$-computable numberings,
by S. Podzorov,
(pdf), preprint submitted to
Algebra and Logic, On the definition of Lachlan semilattice,
by S. Podzorov,
(pdf), preprint submitted to
Siberian Mathematical Journal, Proceedings of the Workshop “Computability and models”,
by
(pdf), Almaty, June 24-28, 2002, Can partial numberings be totalised?,
by D. Spreen,
The Journal of Symbolic
Logic , Vol. 66, No. 1, pp. 1157-1185, (2001)
On a Hierarchy of Groups of Computable Automorphisms,
by A.N. Buzykaeva, A. S. Morozov,
( pdf),
Siberian Mathematical Journal, Vol. 43, No. 1, pp. 124 – 127, (2002)
Minimal coverings in the Rogers semilattices,
by S.Badaev, S.Podzorov,
Siberian Mathematical Journal, Vol. 43, No. 4, pp. 616-622, (2002)