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Published online by Cambridge University Press:  11 June 2021

Antonio Montalbán
Antonio Montalbán
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University of California, Berkeley
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Computable Structure Theory
Within the Arithmetic
 , pp. 177 - 186
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References

ANDREWS, URI, CAI, MINGZHONG, SH. KALIMULLIN, ISKANDER, LEMPP, STEFFEN, MILLER, JOSEPH S., and MONTALBÁN, ANTONIO, The complements of lower cones of degrees and the degree spectra of structures, The Journal of Symbolic Logic, vol. 81 (2016), no. 3, pp. 997–1006.CrossRefGoogle Scholar
ANDREWS, URI, GANCHEV, HRISTO, KUYPER, RUITGER, LEMPP, STEFFEN, MILLER, JOSEPH S., SOSKOVA, ALEXANDRA A., and SOSKOVA, MARIYA I., On cototality and the skip operator in the enumeration degrees, submitted for publication.Google Scholar
ANDREWS, URI and MILLER, JOSEPH S., Spectra of theories and structures, Proceedings of the American Mathematical Society, vol. 143 (2015), no. 3, pp. 1283–1298.Google Scholar
ASH, CHRIS, KNIGHT, JULIA, MANASSE, MARK, and SLAMAN, THEODORE, Generic copies of countable structures, Annals of Pure and Applied Logic, vol. 42 (1989), no. 3, pp. 195–205.CrossRefGoogle Scholar
ASH, CHRIS J. and KNIGHT, JULIA, Computable Structures and the Hyperarithmetical Hierarchy, Elsevier Science, 2000.Google Scholar
BADAEV, SERIKZHAN A., Computable enumerations of families of general recursive functions, Algebra i Logika, vol. 16 (1977), no. 2, pp. 129–148, 249.Google Scholar
BALEVA, VESSELA, The jump operation for structure degrees, Archive for Mathematical Logic, vol. 45 (2006), no. 3, pp. 249–265.CrossRefGoogle Scholar
BARWISE, JON, Infinitary logic and admissible sets, The Journal of Symbolic Logic, vol. 34 (1969), no. 2, pp. 226–252.Google Scholar
BARWISE, JON, Admissible Sets and Structures, Springer-Verlag, Berlin, 1975, An approach to definability theory, Perspectives in Mathematical Logic.CrossRefGoogle Scholar
BELJAEV, V. JA. and ABRAMOVICH TAĬCLIN, MIKHAIL, Elementary properties of existentially closed systems, Uspekhi Mat. Nauk, vol. 34 (1979), no. 2(206), pp. 39–94.Google Scholar
CALVERT, WESLEY, CUMMINS, DESMOND, KNIGHT, JULIA F., and MILLER, SARA, Comparison of classes of finite structures, Algebra Logika, vol. 43 (2004), no. 6, pp. 666–701, 759.Google Scholar
CALVERT, WESLEY, HARIZANOV, VALENTINA, and SHLAPENTOKH, ALEXANDRA, Turing degrees of isomorphism types of algebraic objects, Journal of the London Mathematical Society (2), vol. 75 (2007), no. 2, pp. 273–286.CrossRefGoogle Scholar
CHISHOLM, JOHN, Effective model theory vs. recursive model theory, The Journal of Symbolic Logic, vol. 55 (1990), no. 3, pp. 1168–1191.Google Scholar
COOPER, S. BARRY, Computability Theory, Chapman & Hall/ CRC, Boca Raton, FL, 2004.Google Scholar
CUTLAND, NIGEL, Computability, Cambridge University Press, Cambridge-New York, 1980.Google Scholar
DOWNEY, RODNEY G., HIRSCHFELDT, DENIS R., KACH, ASHER M., LEMPP, STEFFEN, MILETI, JOSEPH R., and MONTALBÁN, ANTONIO, Subspaces of computable vector spaces, Journal of Algebra, vol. 314 (2007), no. 2, pp. 888–894.Google Scholar
DOWNEY, RODNEY G., HIRSCHFELDT, DENIS R., and KHOUSSAINOV, BAKHADYR, Uniformity in the theory of computable structures, Algebra Logika, vol. 42 (2003), no. 5, pp. 566–593, 637.Google Scholar
DOWNEY, RODNEY G. and JOCKUSCH, CARL G., Every low Boolean algebra is isomorphic to a recursive one, Proceedings of the American Mathematical Society, vol. 122 (1994), no. 3, pp. 871–880.Google Scholar
DOWNEY, RODNEY G., KACH, ASHER M., LEMPP, STEFFEN, LEWIS-PYE, ANDREW E. M., MONTALBÁN, ANTONIO, and TURETSKY, DANIEL D., The complexity of computable categoricity, Advances in Mathematics, vol. 268 (2015), pp. 423–466.Google Scholar
DOWNEY, RODNEY G., KACH, ASHER M., LEMPP, STEFFEN, and TURETSKY, DANIEL D., Computable categoricity versus relative computable categoricity, Fundamenta Mathematicae, vol. 221 (2013), no. 2, pp. 129– 159.Google Scholar
DOWNEY, RODNEY G. and KNIGHT, JULIA F., Orderings with αth jump degree 0(α), Proceedings of the American Mathematical Society, vol. 114 (1992), no. 2, pp. 545–552.Google Scholar
ENDERTON, HERBERT B., Computability Theory, Elsevier, Academic Press, Amsterdam, 2011.Google Scholar
ERSHOV, YURI L., Theorie der Numerierungen. III, Z. Math. Logik Grundlagen Math., vol. 23 (1977), no. 4, pp. 289–371, Translated from the Russian and edited by G. Asser and H.-D. Hecker.Google Scholar
ERSHOV, YURI L., Definability and Computability, Siberian School of Algebra and Logic, Consultants Bureau, New York, 1996.Google Scholar
FAIZRAHMANOV, MARAT and KALIMULLIN, ISKANDER, Limitwise monotonic sets of reals, submitted for publication.Google Scholar
FELLNER, STEPHEN MARTIN, Recursiveness and Finite Axiomatizability of Linear Orderings, Ph.D. thesis, Rutgers, The State University of New Jersey, New Brunswick, 1976.Google Scholar
FOKINA, EKATERINA B. and FRIEDMAN, SY-DAVID, Equivalence relations on classes of computable structures, Mathematical Theory and Computational Practice, Lecture Notes in Computer Science, vol. 5635, Springer, Berlin, 2009, pp. 198–207.Google Scholar
FOKINA, EKATERINA B., FRIEDMAN, SY-DAVID, HARIZANOV, VALENTINA, KNIGHT, JULIA F., MCCOY, CHARLES, and MONTALBÁN, ANTONIO, Isomorphism relations on computable structures, The Journal of Symbolic Logic, vol. 77 (2012), no. 1, pp. 122–132.Google Scholar
FRIEDBERG, RICHARD M., A criterion for completeness of degrees of unsolvability, The Journal of Symbolic Logic, vol. 22 (1957), pp. 159–160.CrossRefGoogle Scholar
FRIEDBERG, RICHARD M., Two recursively enumerable sets of incomparable degrees of unsolvability (solution of Post’s problem, 1944), Proc. Nat. Acad. Sci. U.S.A., vol. 43 (1957), pp. 236–238.CrossRefGoogle ScholarPubMed
FRIEDMAN, HARVEY and STANLEY, LEE, A Borel reducibility theory for classes of countable structures, The Journal of Symbolic Logic, vol. 54 (1989), no. 3, pp. 894–914.Google Scholar
FRIEDMAN, HARVEY M., SIMPSON, STEPHEN G., and SMITH, RICK L., Countable algebra and set existence axioms, Annals of Pure and Applied Logic, vol. 25 (1983), no. 2, pp. 141–181.Google Scholar
FROLOV, ANDREY, KALIMULLIN, ISKANDER, and MILLER, RUSSELL, Spectra of algebraic fields and subfields, Mathematical Theory and Computational Practice, Lecture Notes in Comput. Sci., vol. 5635, Springer, Berlin, 2009, pp. 232–241.Google Scholar
GONCHAROV, SERGEY S., Selfstability, and computable families of constructivizations, Algebra i Logika, vol. 14 (1975), no. 6, pp. 647–680, 727.Google Scholar
GONCHAROV, SERGEY S., Some properties of the constructivization of boolean algebras, Sibirskii Matematicheskii Zhurnal, vol. 16 (1975), no. 2, pp. 264– 278.Google Scholar
GONCHAROV, SERGEY S., The number of nonautoequivalent constructivizations, Algebra i Logika, vol. 16 (1977), no. 3, pp. 257–282, 377.Google Scholar
GONCHAROV, SERGEY S., Autostability of models and abelian groups, Algebra i Logika, vol. 19 (1980), no. 1, pp. 23–44, 132.Google Scholar
GONCHAROV, SERGEY S. and DZGOEV, V. D., Autostability of models, Algebra i Logika, vol. 19 (1980), no. 1, pp. 45–58, 132.Google Scholar
GONCHAROV, SERGEY S., HARIZANOV, VALENTINA, KNIGHT, JULIA, MCCOY, CHARLES, MILLER, RUSSELL, and SOLOMON, REED, Enumerations in computable structure theory, Annals of Pure and Applied Logic, vol. 136 (2005), no. 3, pp. 219–246.CrossRefGoogle Scholar
GONCHAROV, SERGEY S., LEMPP, STEFFEN, and SOLOMON, REED, The computable dimension of ordered abelian groups, Advances in Mathematics, vol. 175 (2003), no. 1, pp. 102–143.CrossRefGoogle Scholar
GONCHAROV, SERGEY S. and NAĬT, DZH., Computable structure and antistructure theorems, Algebra Logika, vol. 41 (2002), no. 6, pp. 639– 681, 757.Google Scholar
GORDON, CARL E., Comparisons between some generalizations of recursion theory, Compositio Math., vol. 22 (1970), pp. 333–346.Google Scholar
HARRINGTON, LEO, Analytic determinacy and 0♯, The Journal of Symbolic Logic, vol. 43 (1978), no. 4, pp. 685–693.Google Scholar
HARRIS, KENNETH and MONTALBÁN, ANTONIO, On the n-back-and-forth types of Boolean algebras, Transactions of the American Mathematical Society, vol. 364 (2012), no. 2, pp. 827–866.Google Scholar
HARRIS, KENNETH and MONTALBÁN, ANTONIO, Boolean algebra approximations, Transactions of the American Mathematical Society, vol. 366 (2014), no. 10, pp. 5223–5256.CrossRefGoogle Scholar
HARRISON-TRAINOR, MATTHEW, MELNIKOV, ALEXANDER, MILLER, RUSSELL, and MONTALBÁN, ANTONIO, Computable functors and effective interpretability, submitted for publication.Google Scholar
HARRISON-TRAINOR, MATTHEW, MILLER, RUSSELL, and MONTALBÁN, ANTONIO, Generic functors and infinitary interpretations, in preparation.Google Scholar
HARRISON-TRAINOR, MATTHEW and MONTALBÁN, ANTONIO, The tree of tuples of a structure, submitted for publication.Google Scholar
HERWIG, BERNHARD, LEMPP, STEFFEN, and ZIEGLER, MARTIN, Constructive models of uncountably categorical theories, Proceedings of the American Mathematical Society, vol. 127 (1999), no. 12, pp. 3711–3719.Google Scholar
HIGMAN, GRAHAM, Ordering by divisibility in abstract algebras, Proceedings of the London Mathematical Society (3), vol. 2 (1952), pp. 326– 336.Google Scholar
HIRSCHFELDT, DENIS R., Computable trees, prime models, and relative decidability, Proceedings of the American Mathematical Society, vol. 134 (2006), no. 5, pp. 1495–1498.Google Scholar
HIRSCHFELDT, DENIS R., KHOUSSAINOV, BAKHADYR, SHORE, RICHARD A., and SLINKO, ARKADII M., Degree spectra and computable dimensions in algebraic structures, Annals of Pure and Applied Logic, vol. 115 (2002), no. 1-3, pp. 71–113.Google Scholar
HIRSCHFELDT, DENIS R. and SHORE, RICHARD A., Combinatorial principles weaker than Ramsey’s theorem for pairs, The Journal of Symbolic Logic, vol. 72 (2007), no. 1, pp. 171–206.Google Scholar
JOCKUSCH, CARL G. JR., Semirecursive sets and positive reducibility, Transactions of the American Mathematical Society, vol. 131 (1968), pp. 420–436.Google Scholar
JOCKUSCH, CARL G. JR., Degrees of generic sets, Recursion Theory: Its Generalisation and Applications (Proc. Logic Colloq., Univ. Leeds, Leeds, 1979), London Mathematical Society Lecture Note Series, vol. 45, Cambridge University Press, Cambridge – New York, 1980, pp. 110–139.Google Scholar
JOCKUSCH, CARL G. JR. and SOARE, ROBERT I., Degrees of orderings not isomorphic to recursive linear orderings, Annals of Pure and Applied Logic, vol. 52 (1991), no. 1-2, pp. 39–64, International Symposium on Mathematical Logic and its Applications (Nagoya, 1988).Google Scholar
KACH, ASHER and MONTALBÁN, ANTONIO, Linear orders with finitely many descending cuts, in preparation.Google Scholar
KALIMULLIN, ISKANDER SH., Almost computably enumerable families of sets, Mat. Sb., vol. 199 (2008), no. 10, pp. 33–40.Google Scholar
KALIMULLIN, ISKANDER SH., Uniform reducibility of representability problems for algebraic structures., Sibirskii Matematicheskii Zhurnal, vol. 50 (2009), no. 2, pp. 334–343.Google Scholar
KHISAMIEV, A. N., On the Ershov upper semilattice LE, Sibirsk. Mat. Zh., vol. 45 (2004), no. 1, pp. 211–228.Google Scholar
KHOUSSAINOV, BAKHADYR, SEMUKHIN, PAVEL, and STEPHAN, FRANK, Applications of Kolmogorov complexity to computable model theory, The Journal of Symbolic Logic, vol. 72 (2007), no. 3, pp. 1041– 1054.Google Scholar
KHOUSSAINOV, BAKHADYR and SHORE, RICHARD A., Computable isomorphisms, degree spectra of relations, and Scott families, Annals of Pure and Applied Logic, vol. 93 (1998), no. 1-3, pp. 153–193.Google Scholar
KLEENE, STEPHEN C. and POST, EMIL L., The upper semi-lattice of the degrees of recursive unsolvability, Annals of Mathematics, vol. 59 (1954), pp. 379–407.Google Scholar
KNIGHT, JULIA F., Degrees coded in jumps of orderings, The Journal of Symbolic Logic, vol. 51 (1986), no. 4, pp. 1034–1042.Google Scholar
KNIGHT, JULIA F., Degrees of models, Handbook of Recursive Mathematics, Vol. 1, Stud. Logic Found. Math., vol. 138, North-Holland, Amsterdam, 1998, pp. 289–309.Google Scholar
KNIGHT, JULIA F., MILLER, SARA, and BOOM, M. VANDEN, Turing computable embeddings, The Journal of Symbolic Logic, vol. 72 (2007), no. 3, pp. 901–918.Google Scholar
KNIGHT, JULIA F. and STOB, MICHAEL, Computable Boolean algebras, The Journal of Symbolic Logic, vol. 65 (2000), no. 4, pp. 1605– 1623.Google Scholar
KRUSKAL, JOSEPH B., Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture, Transactions of the American Mathematical Society, vol. 95 (1960), pp. 210–225.Google Scholar
KUDINOV, OLEG V., An autostable 1-decidable model without a computable Scott family of ∃-formulas, Algebra i Logika, vol. 35 (1996), no. 4, pp. 458–467, 498.Google Scholar
KUDINOV, OLEG V., Some properties of autostable models, Algebra i Logika, vol. 35 (1996), no. 6, pp. 685–698, 752.Google Scholar
KUDINOV, OLEG V., The problem of describing autostable models, Algebra i Logika, vol. 36 (1997), no. 1, pp. 26–36, 117.Google Scholar
LA ROCHE, PETER E., Contributions to Recursive Algebra, Ph.D. thesis, Cornell University, 1978, p. 33.Google Scholar
LACHLAN, ALISTAIR H., The priority method for the construction of recursively enumerable sets, Cambridge Summer School in Mathematical Logic (Cambridge, 1971), Springer, Berlin, 1973, pp. 299–310. Lecture Notes in Math., Vol. 337.Google Scholar
LAVROV, IGOR A., The effective non-separability of the set of identically true formulae and the set of finitely refutable formulae for certain elementary theories, Algebra i Logika Sem., vol. 2 (1963), no. 1, pp. 5–18.Google Scholar
LEMPP, STEFFEN, MCCOY, CHARLES, MILLER, RUSSELL, and SOLOMON, REED, Computable categoricity of trees of finite height, The Journal of Symbolic Logic, vol. 70 (2005), no. 1, pp. 151–215.CrossRefGoogle Scholar
LERMAN, MANUEL, Degrees of Unsolvability, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1983, Local and global theory.Google Scholar
LOPEZ-ESCOBAR, EDGAR G. K., On defining well-orderings, Fundamenta Mathematicae, vol. 59 (1966), pp. 13–21.Google Scholar
MAL’CEV, ANATOLII I., On recursive Abelian groups, Dokl. Akad. Nauk SSSR, vol. 146 (1962), pp. 1009–1012.Google Scholar
MARKER, DAVID, Degrees of models of true arithmetic, Proceedings of the Herbrand symposium (Marseilles, 1981), Stud. Logic Found. Math., vol. 107, North-Holland, Amsterdam, 1982, pp. 233–242.Google Scholar
MARKER, DAVID and MILLER, RUSSELL, Turing degree spectra of differentially closed fields, The Journal of Symbolic Logic, vol. 82 (2017), no. 1, pp. 1–25.Google Scholar
MARTIN, DONALD A., The axiom of determinateness and reduction principles in the analytical hierarchy, Bulletin of the American Mathematical Society, vol. 74 (1968), pp. 687–689.Google Scholar
MARTIN, DONALD A., Borel determinacy, Annals of Mathematics (2), vol. 102 (1975), no. 2, pp. 363–371.CrossRefGoogle Scholar
MCCARTHY, ETHAN, Cototal enumeration degrees and the Turing degree spectra of minimal subshifts, to appear in the Proceedings of the American Mathematical Society DOI: 10.1090/proc/13783.Google Scholar
MCCOY, CHARLES F. D., Δ20-categoricity in Boolean algebras and linear orderings, Annals of Pure and Applied Logic, vol. 119 (2003), no. 1-3, pp. 85–120.Google Scholar
MEDVEDEV, YURI T., Degrees of difficulty of the mass problem, Dokl. Akad. Nauk SSSR (N.S.), vol. 104 (1955), pp. 501–504.Google Scholar
MELNIKOV, ALEXANDER and MONTALBÁN, ANTONIO, Computable polish group actions, The Journal of Symbolic Logic, vol. 83 (2018), no. 2, pp. 443–460.Google Scholar
METAKIDES, GEORGE and NERODE, ANIL, Effective content of field theory, Annals of Mathematical Logic, vol. 17 (1979), no. 3, pp. 289–320.Google Scholar
MILLAR, TERRENCE, Omitting types, type spectrums, and decidability, The Journal of Symbolic Logic, vol. 48 (1983), no. 1, pp. 171–181.Google Scholar
MILLER, JOSEPH S., Degrees of unsolvability of continuous functions, The Journal of Symbolic Logic, vol. 69 (2004), no. 2, pp. 555–584.Google Scholar
MILLER, RUSSELL, POONEN, BJORN, SCHOUTENS, HANS, and SHLAPENTOKH, ALEXANDRA, A computable functor from graphs to fields, to appear.Google Scholar
MONTALBÁN, ANTONIO, Notes on the jump of a structure, Mathematical Theory and Computational Practice, (2009), pp. 372–378.Google Scholar
MONTALBÁN, ANTONIO, Counting the back-and-forth types, Journal of Logic and Computability, (2010), pp. 857–876, doi: 10.1093/logcom/exq048.Google Scholar
MONTALBÁN, ANTONIO, Rice sequences of relations, Philosophical Transactions of the Royal Society A, vol. 370 (2012), pp. 3464–3487.Google Scholar
MONTALBÁN, ANTONIO, A computability theoretic equivalent to Vaught’s conjecture, Advances in Mathematics, vol. 235 (2013), pp. 56–73.Google Scholar
MONTALBÁN, ANTONIO, Copyable structures, The Journal of Symbolic Logic, vol. 78 (2013), no. 4, pp. 1025–1346.Google Scholar
MONTALBÁN, ANTONIO, A fixed point for the jump operator on structures, The Journal of Symbolic Logic, vol. 78 (2013), no. 2, pp. 425–438.Google Scholar
MONTALBÁN, ANTONIO, Computability theoretic classifications for classes of structures, Proceedings of ICM 2014, vol. 2 (2014), pp. 79–101.Google Scholar
MONTALBÁN, ANTONIO, Priority arguments via true stages, The Journal of Symbolic Logic, vol. 79 (2014), no. 4, pp. 1315–1335.Google Scholar
MONTALBÁN, ANTONIO, Analytic equivalence relations satisfying hyperarith-metic-is-recursive, Forum Math. Sigma, vol. 3 (2015), pp. e8, 11.Google Scholar
MONTALBÁN, ANTONIO, Classes of structures with no intermediate isomorphism problems, The Journal of Symbolic Logic, vol. 81 (2016), no. 1, pp. 127–150.CrossRefGoogle Scholar
MONTALBÁN, ANTONIO, Effectively existentially-atomic structures, Computability and Complexity, Lecture Notes in Computer Science, vol. 10010, Springer, 2016, pp. 221–237.Google Scholar
MONTALBÁN, ANTONIO, Computable Structure Theory: Beyond the arithmetic, Cambridge University Press, P2, in preparation.Google Scholar
MONTALBÁN, ANTONIO and SHORE, RICHARD A., The limits of determinacy in second order arithmetic, Proceedings of the London Mathematical Society, vol. 104 (2012), no. 2, pp. 223–252.Google Scholar
MORLEY, MICHAEL, Omitting classes of elements, Theory of Models (Proc. 1963 Internat. Sympos. Berkeley), North-Holland, Amsterdam, 1965, pp. 265–273.Google Scholar
MOROZOV, ANDREI S., On the relation of Σ-reducibility between admissible sets, Sibirsk. Mat. Zh., vol. 45 (2004), no. 3, pp. 634–652.Google Scholar
MOSCHOVAKIS, YIANNIS N., Abstract first order computability. I, II, Transactions of the American Mathematical Society, vol. 138 (1969), pp. 427–464.Google Scholar
MUCHNIK, ALBERT A., On the unsolvability of the problem of reducibility in the theory of algorithms, Dokl. Akad. Nauk SSSR, N.S., vol. 108 (1956), pp. 194–197.Google Scholar
MUCHNIK, ALBERT A., On strong and weak reducibility of algorithmic problems, Sibirsk. Mat. Ž., vol. 4 (1963), pp. 1328–1341.Google Scholar
NIES, ANDRÉ, Computability and Randomness, Oxford Logic Guides, vol. 51, Oxford University Press, Oxford, 2009.Google Scholar
NURTAZIN, ABYZ T., Strong and weak constructivizations, and enumerable families, Algebra i Logika, vol. 13 (1974), pp. 311–323, 364.Google Scholar
POST, EMIL L., Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 284–316.Google Scholar
POUZET, MAURICE, Modèle universel d’une théorie n-complète: Modèle uniformément préhomogène, Comptes Rendus Hebdomadaires des Séances de l’Academie des Sciences, Série A-B, vol. 274 (1972), pp. A695– A698.Google Scholar
PUZARENKO, VADIM, On a certain reducibility on admissible sets, Sibirsk. Mat. Zh., vol. 50 (2009), no. 2, pp. 415–429.Google Scholar
PUZARENKO, VADIM, Fixed points of the jump operator, Algebra and Logic, vol. 5 (2011), pp. 418–438.Google Scholar
RABIN, MICHAEL O. and SCOTT, DANA, The undecidability of some simple theories, unpublished notes.Google Scholar
REMMEL, JEFFREY B., Recursive Boolean algebras with recursive atoms, The Journal of Symbolic Logic, vol. 46 (1981), no. 3, pp. 595–616.Google Scholar
REMMEL, JEFFREY B., Recursively categorical linear orderings, Proceedings of the American Mathematical Society, vol. 83 (1981), no. 2, pp. 387–391.Google Scholar
RICHTER, LINDA, Degrees of Unsolvability of Models, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1977.Google Scholar
RICHTER, LINDA, Degrees of structures, The Journal of Symbolic Logic, vol. 46 (1981), no. 4, pp. 723–731.Google Scholar
SCHWEBER, NOAH, Interactions Between Computability Theory and Set Theory, Ph.D. thesis, University of California, Berkeley, 2016, p. 137.Google Scholar
SELMAN, ALAN L., Arithmetical reducibilities. I, Z. Math. Logik Grundlagen Math., vol. 17 (1971), pp. 335–350.Google Scholar
SHORE, RICHARD A., Controlling the dependence degree of a recursively enumerable vector space, The Journal of Symbolic Logic, vol. 43 (1978), no. 1, pp. 13–22.Google Scholar
SIMMONS, HAROLD, Large and small existentially closed structures, The Journal of Symbolic Logic, vol. 41 (1976), no. 2, pp. 379–390.Google Scholar
SLAMAN, THEODORE A., Relative to any nonrecursive set, Proceedings of the American Mathematical Society, vol. 126 (1998), no. 7, pp. 2117–2122.CrossRefGoogle Scholar
SMITH, RICK L., Two theorems on autostability in p-groups, Logic Year 1979–80 (Proc. Seminars and Conf. Math. Logic, Univ. Connecticut, Storrs, Conn., 1979/80), Lecture Notes in Math., vol. 859, Springer, Berlin, 1981, pp. 302–311.Google Scholar
SOARE, ROBERT I., Turing Computability, Theory and Applications of Computability, Springer-Verlag, Berlin, 2016, Theory and applications.Google Scholar
SOSKOV, IVAN N., Degree spectra and co-spectra of structures, Annuaire Univ. Sofia Fac. Math. Inform., vol. 96 (2004), pp. 45–68.Google Scholar
SOSKOVA, ALEXANDRA A., A jump inversion theorem for the degree spectra, Proceedings of CiE 2007, Lecture Notes in Computer Science, vol. 4497, Springer-Verlag, 2007, pp. 716–726.Google Scholar
SOSKOVA, ALEXANDRA A. and SOSKOV, IVAN N., A jump inversion theorem for the degree spectra, Journal of Logic and Computation, vol. 19 (2009), no. 1, pp. 199–215.Google Scholar
STEINER, REBECCA M., Effective algebraicity, Archive for Mathematical Logic, vol. 52 (2013), no. 1-2, pp. 91–112.Google Scholar
STUKACHEV, ALEKSEY I., Degrees of presentability of models. I, Algebra Logika, vol. 46 (2007), no. 6, pp. 763–788, 793–794.Google Scholar
STUKACHEV, ALEKSEY I., A jump inversion theorem for semilattices of Σ-degrees, Sib. Èlektron. Mat. Izv., vol. 6 (2009), pp. 182–190.Google Scholar
STUKACHEV, ALEKSEY I., A jump inversion theorem for the semilattices of Sigma-degrees [translation of mr2586684], Siberian Advances in Mathematics, vol. 20 (2010), no. 1, pp. 68–74.CrossRefGoogle Scholar
STUKACHEV, ALEKSEY I., Effective model theory: approach via σ-definability, Effective Mathematics of the Uncountable (Noam Greenberg, Denis Hirschfeldt, Joel David Hamkins, and Russell Miller, editors), Lecture Notes in Logic, vol. 41, Cambridge University Press, 2013, pp. 164–197.Google Scholar
SUSLIN, MIKHAIL YA., Sur un définition des ensembles measurables B sans nombres transfinis, Comptes Rendus de l’Academie des Sciences Paris, vol. 164 (1917), pp. 88–91.Google Scholar
THURBER, JOHN J., Every low2 Boolean algebra has a recursive copy, Proceedings of the American Mathematical Society, vol. 123 (1995), no. 12, pp. 3859–3866.Google Scholar
VAĬTSENAVICHYUS, RIMANTAS, Inner-resolvent feasible sets, Mat. Logika Primenen., vol. 1 (1989), no. 6, pp. 9–20.Google Scholar
VATEV, STEFAN, Conservative extensions of abstract structures, CiE (Benedikt Löwe, Dag Normann, Ivan N. Soskov, and Alexandra A. Soskova, editors), Lecture Notes in Computer Science, vol. 6735, Springer, 2011, pp. 300–309.Google Scholar
VENTSOV, YURI G., The effective choice problem for relations and reducibilities in classes of constructive and positive models, Algebra i Logika, vol. 31 (1992), no. 2, pp. 101–118, 220.Google Scholar
WEHNER, STEPHAN, Enumerations, countable structures and Turing degrees, Proceedings of the American Mathematical Society, vol. 126 (1998), no. 7, pp. 2131–2139.Google Scholar

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  • Antonio Montalbán, University of California, Berkeley
  • Book: Computable Structure Theory
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  • Chapter DOI: https://doi.org/10.1017/9781108525749.012
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  • Bibliography
  • Antonio Montalbán, University of California, Berkeley
  • Book: Computable Structure Theory
  • Online publication: 11 June 2021
  • Chapter DOI: https://doi.org/10.1017/9781108525749.012
Available formats
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  • Bibliography
  • Antonio Montalbán, University of California, Berkeley
  • Book: Computable Structure Theory
  • Online publication: 11 June 2021
  • Chapter DOI: https://doi.org/10.1017/9781108525749.012
Available formats
×