S. A. Badaev, S. S. Goncharov, A. Sorbi, “Elementary Theories for Rogers Semilattices”, Algebra Logika, 44:3 (2005), 261–268; Algebra and Logic, 44:3 (2006), 143

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Algebra i logika, 2005, Volume 44, Number 3, Pages 261–268 (Mi al110)

This article is cited in 15 scientific papers (total in 15 papers)

Elementary Theories for Rogers Semilattices

S. A. Badaev^a, S. S. Goncharov^b, A. Sorbi^c

^a Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^c Dipartimento di Scienze Matematiche ed Informatiche Roberto Magari, Università degli Studi di Sienna

Full-text PDF (158 kB) Citations (15)

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Abstract: It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.

Keywords: arithmetic hierarchy, Rogers semilattice, elementary theory.

Received: 25.02.2003
Revised: 12.07.2004

English version:
Algebra and Logic, 2006, Volume 44, Issue 3, Pages 143–147
DOI: https://doi.org/10.1007/s10469-005-0016-x

Bibliographic databases:

UDC: 510.55

Language: Russian

Citation: S. A. Badaev, S. S. Goncharov, A. Sorbi, “Elementary Theories for Rogers Semilattices”, Algebra Logika, 44:3 (2005), 261–268; Algebra and Logic, 44:3 (2006), 143–147

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/al110

https://www.mathnet.ru/eng/al/v44/i3/p261

This publication is cited in the following 15 articles:

Nikolay Bazhenov, Manat Mustafa, Anvar Nurakunov, “On Concept Lattices for Numberings”, Tsinghua Sci. Technol., 29:6 (2024), 1642
M. Kh. Faizrakhmanov, “Effektivno beskonechnye klassy numeratsii vychislimykh semeistv deistvitelnykh chisel”, Izv. vuzov. Matem., 2023, no. 5, 96–100
M. Kh. Faizrahmanov, “Effectively Infinite Classes of Numberings of Computable Families of Reals”, Russ Math., 67:5 (2023), 72
Nikolay Bazhenov, Manat Mustafa, Zhansaya Tleuliyeva, “Rogers semilattices of limitwise monotonic numberings”, Mathematical Logic Qtrly, 68:2 (2022), 213
Bazhenov N.A., Mustafa M., Tleuliyeva Zh., “Theories of Rogers Semilattices of Analytical Numberings”, Lobachevskii J. Math., 42:4, SI (2021), 701–708
S. S. Ospichev, “Fridbergovy numeratsii semeistv chastichno vychislimykh funktsionalov”, Sib. elektron. matem. izv., 16 (2019), 331–339
Bazhenov N., Mustafa M., Yamaleev M., “Elementary Theories and Hereditary Undecidability For Semilattices of Numberings”, Arch. Math. Log., 58:3-4 (2019), 485–500
S. A. Badaev, A. A. Issakhov, “Some absolute properties of $A$-computable numberings”, Algebra and Logic, 57:4 (2018), 275–288
M. Kh. Faizrahmanov, “Minimal generalized computable enumerations and high degrees”, Siberian Math. J., 58:3 (2017), 553–558
M. Kh. Faizrakhmanov, “Universal computable enumerations of finite classes of families of total functions”, Russian Math. (Iz. VUZ), 60:12 (2016), 79–83
S. S. Ospichev, “Computable families of sets in Ershov hierarchy without principal numberings”, J. Math. Sci., 215:4 (2016), 529–536
S. A. Badaev, S. S. Goncharov, “Generalized computable universal numberings”, Algebra and Logic, 53:5 (2014), 355–364
Serikzhan Badaev, Sergey Goncharov, New Computational Paradigms, 2008, 19
S. A. Badaev, S. S. Goncharov, A. Sorbi, “Isomorphism types of Rogers semilattices for families from different levels of the arithmetical hierarchy”, Algebra and Logic, 45:6 (2006), 361–370
Badaev S.A., Talasbaeva Zh.T., “Computable numberings in the hierarchy of Ershov”, Mathematical Logic in Asia, 2006, 17–30

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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