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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 4, Pages 735–749 (Mi izv1489)  

This article is cited in 23 scientific papers (total in 24 papers)

Decidability of the universal and positive theories of a free group

G. S. Makanin


Abstract: The decidability of the universal and positive theories of a free group is established.
Bibliography: 3 titles.

Full text: PDF file (1460 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1985, 25:1, 75–88

Bibliographic databases:

Document Type: Article
UDC: 512
MSC: Primary 20F10; Secondary 03B25
Received: 07.04.1983

Citation: G. S. Makanin, “Decidability of the universal and positive theories of a free group”, Izv. Akad. Nauk SSSR Ser. Mat., 48:4 (1984), 735–749; Math. USSR-Izv., 25:1 (1985), 75–88

Citation in format AMSBIB
\Bibitem{Mak84}
\by G.~S.~Makanin
\paper Decidability of the universal and positive theories of a~free group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 4
\pages 735--749
\mathnet{http://mi.mathnet.ru/izv1489}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=755956}
\zmath{https://zbmath.org/?q=an:0578.20001}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 1
\pages 75--88
\crossref{https://doi.org/10.1070/IM1985v025n01ABEH001269}


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    1. V. D. Mazurov, “Solved problems in the Kourovka Notebook”, Russian Math. Surveys, 46:5 (1991), 137–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. M. Gaglione, D. Spellman, “Generalizations of free groups: some questions”, Communications in Algebra, 22:8 (1994), 3159  crossref
    3. V. G. Durnev, “On elementary theories of integer linear groups”, Izv. Math., 59:5 (1995), 919–934  mathnet  crossref  mathscinet  zmath  isi
    4. V. G. Durnev, “On the solvability problem for equations with a single coefficient”, Math. Notes, 59:6 (1996), 601–610  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Olivier Chapuis, “∀-free metabelian groups”, J. symb. log, 62:01 (1997), 159  crossref
    6. A KHELIF, “Le passage d'un groupe libre à sa complétion profinie: étude logique”, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 326:3 (1998), 281  crossref
    7. Antoni Kościelski, Leszek Pacholski, “Makanin's algorithm is not primitive recursive”, Theoretical Computer Science, 191:1-2 (1998), 145  crossref
    8. O. Kharlampovich, A. Myasnikov, “Irreducible Affine Varieties over a Free Group”, Journal of Algebra, 200:2 (1998), 517  crossref
    9. Anatole Khelif, “Finite approximation and commutators in free groups”, Journal of Algebra, 281:2 (2004), 407  crossref
    10. Z. Sela, “Diophantine geometry over groups III: Rigid and solid solutions”, Isr J Math, 147:1 (2005), 1  crossref  mathscinet  zmath  isi
    11. Dietrich Kuske, Markus Lohrey, “Logical aspects of Cayley-graphs: the group case”, Annals of Pure and Applied Logic, 131:1-3 (2005), 263  crossref
    12. Volker Diekert, Claudio Gutierrez, Christian Hagenah, “The existential theory of equations with rational constraints in free groups is PSPACE-complete”, Information and Computation, 202:2 (2005), 105  crossref
    13. V. G. Durnev, O. V. Zetkina, “On equations in free semigroups with certain constraints on their solutions”, J. Math. Sci. (N. Y.), 158:5 (2009), 671–676  mathnet  crossref  elib  elib
    14. François Dahmani, Daniel Groves, “The isomorphism problem for toral relatively hyperbolic groups”, Publ.math.IHES, 107:1 (2008), 211  crossref
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    16. Tamar Aizikowitz, Nissim Francez, Daniel Genkin, Michael Kaminski, “Extending Free Pregroups with Lower Bounds”, Stud Logica, 2010  crossref
    17. V. G. Durnev, O. V. Zetkina, “Ob uravneniyakh s podpolugruppovymi ogranicheniyami na resheniya v svobodnykh polugruppakh”, Chebyshevskii sb., 11:3 (2010), 78–87  mathnet  zmath
    18. V. G. Durnev, O. V. Zetkina, “Ob uravneniyakh v svobodnoi gruppe s ogranicheniyami na resheniya”, Chebyshevskii sb., 11:3 (2010), 88–97  mathnet  zmath
    19. V. G. Durnev, O. V. Zetkina, “Ob uravneniyakh v svobodnykh gruppakh, razreshennykh otnositelno neizvestnykh, s ogranicheniyami na resheniya”, Chebyshevskii sb., 13:1 (2012), 63–80  mathnet
    20. E.D.. Demaine, M.L.. Demaine, Ya.N.. Minsky, J.S.. B. Mitchell, R.L.. Rivest, “Picture-Hanging Puzzles”, Theory Comput Syst, 2013  crossref
    21. A. N. Shevlyakov, “Unifying solutions to systems of equations in finite simple semigroups”, Algebra and Logic, 53:1 (2014), 70–83  mathnet  crossref  mathscinet  isi
    22. V. G. Durnev, O. V. Zetkina, “Nekotorye rezultaty, poluchennye v Yaroslavskom otdelenii algebraicheskoi shkoly M. D. Grindlingera”, Chebyshevskii sb., 15:4 (2014), 5–31  mathnet
    23. Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, Dennis Spellman, “The Tarski Problems and Their Solutions”, APM, 05:04 (2015), 212  crossref
    24. S. I. Adian, “On the studies of Gennadii Semënovich Makanin on algorithmic questions of the theory of groups and semigroups”, Russian Math. Surveys, 73:3 (2018), 553–568  mathnet  crossref  crossref  adsnasa  isi  elib
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