Geodesic
Difference Hierarchy in $\varphi$-Spaces
Algebra i logika, Tome 43 (2004) no. 4, pp. 425-444.

Voir la notice de l'article provenant de la source Math-Net.Ru

Some results on the Borel and difference hierarchies of subsets in $\varphi$-spaces are established. For instance, we prove analogs of the Hausdorff theorem (relating the difference and Borel hierarchies) and the Lavrentyev theorem (asserting the non-collapse of the difference hierarchy).
Keywords: $\varphi$-space, Borel hierarchy, difference hierarchy. 
@article{AL_2004_43_4_a2,
     author = {V. L. Selivanov},
     title = {Difference {Hierarchy} in $\varphi${-Spaces}},
     journal = {Algebra i logika},
     pages = {425--444},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2004_43_4_a2/}
}
TY  - JOUR
AU  - V. L. Selivanov
TI  - Difference Hierarchy in $\varphi$-Spaces
JO  - Algebra i logika
PY  - 2004
SP  - 425
EP  - 444
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2004_43_4_a2/
LA  - ru
ID  - AL_2004_43_4_a2
ER  - 
%0 Journal Article
%A V. L. Selivanov
%T Difference Hierarchy in $\varphi$-Spaces
%J Algebra i logika
%D 2004
%P 425-444
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2004_43_4_a2/
%G ru
%F AL_2004_43_4_a2
V. L. Selivanov. Difference Hierarchy in $\varphi$-Spaces. Algebra i logika, Tome 43 (2004) no. 4, pp. 425-444. http://geodesic.mathdoc.fr/item/AL_2004_43_4_a2/

[1] Y. N. Moschovakis, Descriptive set theory, North-Holland Publ. Co., Amsterdam, 1980 | MR | Zbl

[2] A. S. Kechris, Classical descriptive set theory, Springer-Verlag, New York, 1994 | MR

[3] Kh. Rodzhers, Teoriya rekursivnykh funktsii i effektivnaya vychislimost, Mir, M., 1972 | MR

[4] A. Tang, “Chain properties in $P_{\omega}$”, Theoret. Comput. Sci., 9 (1979), 153–172 | DOI | MR | Zbl

[5] V. L. Selivanov, “Ob indeksnykh mnozhestvakh v ierarkhii Klini-Mostovskogo”, Matematicheskaya logika i teoriya algoritmov, Trudy In-ta matem. SO AN SSSR, 2, 1982, 135–158 | MR | Zbl

[6] Yu. L. Ershov, Theory of domains and nearby, Lect. Notes Comput. Sci., 735, 1993 | MR

[7] S. Abramsky, A. Jung, “Domain theory”, Handbook of Logic in Computer Science, vol. 3, Oxford, 1994, 1–168 | MR

[8] G. Giertz, K. H. Hoffmann, K. Keimel, J. D. Lawson, M. W. Mislove, D. S. Scott, Continuous lattices and domains, Cambridge, 2003

[9] V. L. Selivanov, “Fine hierarchies and Boolean terms”, J. Symb. Log., 60:1 (1995), 289–317 | DOI | MR | Zbl

[10] V. L. Selivanov, “Indeksnye mnozhestva v giperarifmeticheskoi ierarkhii”, Sib. matem. zh., 25:3 (1984), 164–181 | MR | Zbl

[11] Yu. L. Ershov, “Ob odnoi ierarkhii mnozhestv II”, Algebra i logika, 7:1 (1968), 15–47 | MR | Zbl

[12] K. Kuratovskii, Topologiya, Mir, M., 1969 | MR

[13] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR

[14] V. Stoltenberg-Hansen, J. V. Tucker, “Effective algebras”, Handbook of Logic in Computer Science, vol. 4, 1995, 357–526 | MR

[15] V. L. Selivanov, Hierarchies, numerations, index sets, Handwritten notes, 1992

[16] V. L. Selivanov, “Wadge degrees of $\omega$-languages of deterministic Turing machines”, Theoret. Informatics and Applications, 37 (2003), 67–83 | DOI | MR | Zbl

[17] V. L. Selivanov, Difference hierarchy in $f$-spaces, preprint 02-02, Informatik-Berichte, University of Siegen, 2002 | Zbl