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Algebra Logika, 2004, Volume 43, Number 6, Pages 666–701 (Mi al103)  

This article is cited in 29 scientific papers (total in 29 papers)

Comparing Classes of Finite Structures

W. Calverta, D. Cumminsb, J. F. Knighta, S. Millera

a University of Notre Dame
b University of Illinois at Urbana-Champaign

Abstract: We compare classes of structures using the notion of a computable embedding, which is a partial order on the classes of structures. Our attention is mainly, but not exclusively, focused on classes of finite structures. Also, a number of problems are formulated.

Keywords: computable embedding, finite prime field, finite linear order, finite-dimensional vector space over rationals, linear order

Full text: PDF file (390 kB)
References: PDF file   HTML file

English version:
Algebra and Logic, 2004, 43:6, 374–392

Bibliographic databases:

UDC: 510.53
Received: 20.10.2003

Citation: W. Calvert, D. Cummins, J. F. Knight, S. Miller, “Comparing Classes of Finite Structures”, Algebra Logika, 43:6 (2004), 666–701; Algebra and Logic, 43:6 (2004), 374–392

Citation in format AMSBIB
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\by W.~Calvert, D.~Cummins, J.~F.~Knight, S.~Miller
\paper Comparing Classes of Finite Structures
\jour Algebra Logika
\yr 2004
\vol 43
\issue 6
\pages 666--701
\mathnet{http://mi.mathnet.ru/al103}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2135387}
\zmath{https://zbmath.org/?q=an:1097.03026}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 6
\pages 374--392
\crossref{https://doi.org/10.1023/B:ALLO.0000048827.30718.2c}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750706350}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. W. Calvert, V. S. Harizanova, J. F. Knight, S. Miller, “Index sets of computable structures”, Algebra and Logic, 45:5 (2006), 306–325  mathnet  crossref  mathscinet  zmath
    2. Calvert W., Knight J.F., “Classification from a computable viewpoint”, Bull. Symbolic Logic, 12:2 (2006), 191–218  crossref  mathscinet  zmath  isi  elib  scopus
    3. Stukachev A., “On mass problems of presentability”, Theory and applications of models of computation, Third international conference, TAMC 2006 (Beijing, China, May 15–20, 2006), Proceedings, Lecture Notes in Comput. Sci., 3959, Springer, Berlin, 2006, 772–782  crossref  mathscinet  zmath  isi  scopus
    4. A. I. Stukachev, “Degrees of presentability of structures. I”, Algebra and Logic, 46:6 (2007), 419–432  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    5. E. B. Fokina, “Index sets of decidable models”, Siberian Math. J., 48:5 (2007), 939–948  mathnet  crossref  mathscinet  zmath  isi
    6. Boom M.V., “The effective Borel hierarchy”, Fund. Math., 195:3 (2007), 269–289  crossref  mathscinet  zmath  isi  scopus
    7. Knight J.F., Miller S., Boom M.V., “Turing computable embeddings”, J. Symbolic Logic, 72:3 (2007), 901–918  crossref  mathscinet  zmath  isi  scopus
    8. Chisholm J., Knight J.F., Miller S., “Computable embeddings and strongly minimal theories”, J. Symbolic Logic, 72:3 (2007), 1031–1040  crossref  mathscinet  zmath  isi  scopus
    9. Calvert W., Goncharov S.S., Knight J.F., “Computable structures of Scott rank omega(CK)(1) in familiar classes”, Advances in Logic, Contemporary Mathematics Series, 425, 2007, 49–66  crossref  mathscinet  zmath  adsnasa  isi
    10. Fokina E.B., “Index sets of computable structures with decidable theories”, Computation and Logic in the Real World, Proceedings, Lecture Notes in Computer Science, 4497, 2007, 290–296  crossref  mathscinet  zmath  isi  scopus
    11. E. N. Pavlovskii, “Estimation of the algorithmic complexity of classes of computable models”, Siberian Math. J., 49:3 (2008), 512–523  mathnet  crossref  mathscinet  zmath  isi
    12. Greenberg N., Montalban A., “Ranked structures and arithmetic transfinite recursion”, Trans. Amer. Math. Soc., 360:3 (2008), 1265–1307  crossref  mathscinet  zmath  isi  scopus
    13. E. B. Fokina, “Algoritmicheskie svoistva modelei signatury s dvumya odnomestnymi funktsionalnymi simvolami”, Vestn. NGU. Ser. matem., mekh., inform., 8:1 (2008), 90–101  mathnet
    14. Fokina E.B., “Index sets for some classes of structures”, Ann. Pure Appl. Logic, 157:2-3 (2009), 139–147  crossref  mathscinet  zmath  isi  elib  scopus
    15. Fokina E.B., Friedman S.-D., “Equivalence Relations on Classes of Computable Structures”, Mathematical Theory and Computational Practice, Lecture Notes in Computer Science, 5635, 2009, 198–207  crossref  mathscinet  zmath  isi  scopus
    16. J. Carson, E. Fokina, V. S. Harizanov, J. F. Knight, S. Quinn, C. Safranski, J. Wallbaum, “The computable embedding problem”, Algebra and Logic, 50:6 (2012), 478–493  mathnet  crossref  mathscinet  zmath  isi
    17. Fokina E., Knight J.F., Melnikov A., Quinn S.M., Safranski C., “Classes of Ulm Type and Coding Rank-Homogeneous Trees in Other Structures”, J Symbolic Logic, 76:3 (2011), 846–869  crossref  mathscinet  zmath  isi  elib  scopus
    18. Fokina E.B., Friedman S.-D., “On S11 equivalence relations over the natural numbers”, MLQ Math Log Q, 58:1–2 (2012), 113–124  crossref  mathscinet  zmath  isi  scopus
    19. Fokina E.B., Friedman S.-D., Harizanov V., Knight J.F., McCoy Ch., Montalban A., “Isomorphism Relations on Computable Structures”, J. Symb. Log., 77:1 (2012), 122–132  crossref  mathscinet  zmath  isi  elib  scopus
    20. N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra and Logic, 52:5 (2013), 355–366  mathnet  crossref  mathscinet  isi
    21. Wright M., “Turing Computable Embeddings of Equivalences Other Than Isomorphism”, Proc. Amer. Math. Soc., 142:5 (2014), 1795–1811  crossref  mathscinet  zmath  isi  scopus
    22. Fokina E.B. Harizanov V. Melnikov A., “Computable Model Theory”, Turing'S Legacy: Developments From Turing'S Ideas in Logic, Lecture Notes in Logic, 42, ed. Downey R., Cambridge Univ Press, 2014, 124–194  mathscinet  isi
    23. U. Andrews, D. I. Dushenin, C. Hill, J. F. Knight, A. G. Melnikov, “Comparing classes of finite sums”, Algebra and Logic, 54:6 (2016), 489–501  mathnet  crossref  crossref  mathscinet  isi
    24. M. I. Marchuk, “Index set of structures with two equivalence relations that are autostable relative to strong constructivizations”, Algebra and Logic, 55:4 (2016), 306–314  mathnet  crossref  crossref  isi
    25. Miller R., Ng K.M., “Finitary Reducibility on Equivalence Relations”, J. Symb. Log., 81:4 (2016), 1225–1254  crossref  mathscinet  zmath  isi  scopus
    26. Bazhenov N., “Categoricity Spectra For Polymodal Algebras”, Stud. Log., 104:6 (2016), 1083–1097  crossref  mathscinet  zmath  isi  scopus
    27. Dino Rossegger, “On functors enumerating structures”, Sib. elektron. matem. izv., 14 (2017), 690–702  mathnet  crossref
    28. Knight J.F. Saraph V., “Scott Sentences For Certain Groups”, Arch. Math. Log., 57:3-4 (2018), 453–472  crossref  mathscinet  zmath  isi  scopus
    29. Kalimullin I.Sh., “Computable Embeddings of Classes of Structures Under Enumeration and Turing Operators”, Lobachevskii J. Math., 39:1, SI (2018), 84–88  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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