Preprints and Publications

• A new game metatheorem for Ash-Knight style priority constructions, A. Montalbán
  To appear Proceedings of the program Higher recursion theory and set theory.. 
• The spark of synchronization on heterogeneous network, R. M. Corder and A. Montalbán
  Chaos,    (2024), .
• Emergence of chaotic cluster synchronization in heterogeneous networks, R. M. Corder, Z. Bian, T. Pereira, and A. Montalbán
  Chaos,  33  (2023), .
• The $\omega$-Vaught's Conjecture by, D. Gonzalez and A. Montalban
  Trans. Amer. Math. Soc.,  376  (2023), .
• The structural complexity of models of arithmetic, A. Montalbán and D. Rossegger
  Journal of Symbolic Logic,    (2023), .
• The tree of tuples of a structure, M. Harrison-Trainor and A. Montalban
  J. Symb. Log.,  87  (2022), 21--46.
• Herd immunity under individual variation and reinfection, A. Montalbán, R. M. Corder, and M. G. M. Gomes
  Journal of Mathematical Biology,  85  (2022), .
• Punctual definability on structures, I. Kalimullin, A. Melnikov, and A. Montalban
  Ann. Pure Appl. Logic,  172  (2021), Paper No. 102987, 18.
• The determined property of {B}aire in reverse math, E. P. Astor, D. Dzhafarov, A. Montalban, R. Solomon, and L. B. Westrick
  J. Symb. Log.,  85  (2020), 166--198.
• On the inevitability of the consistency operator, A. Montalbán and J. Walsh
  J. Symb. Log.,  84  (2019), 205--225.
• On the structure of the Wadge degrees of bqo-valued Borel functions, T. Kihara and A. Montalbán
  Trans. Amer. Math. Soc.,  371  (2019), 7885--7923.
• Jump inversions of algebraic structures and {$\Sigma$}-definability, M. Faizrahmanov, A. Kach, I. Kalimullin, A. Montalbán, and V. Puzarenko
  MLQ Math. Log. Q.,  65  (2019), 37--45.
• Martin's Conjecture: A Classification of the Naturally Occurring Turing Degrees, A. Montalbán
  Notices of the American Mathematical Society,  66  (2019), .
• Conservativity of ultrafilters over subsystems of second order arithmetic, A. Montalbán and R. A. Shore
  J. Symb. Log.,  83  (2018), 740--765.
• The uniform {M}artin's conjecture for many-one degrees, T. Kihara and A. Montalbán
  Trans. Amer. Math. Soc.,  370  (2018), 9025--9044.
• Borel functors and infinitary interpretations, M. Harrison-Trainor, R. Miller, and A. Montalbán
  J. Symb. Log.,  83  (2018), 1434--1456.
• Computable Polish group actions, A. Melnikov and A. Montalbán
  J. Symb. Log.,  83  (2018), 443--460.
• Coding and definability in computable structures, A. Montalbán
  Notre Dame J. Form. Log.,  59  (2018), 285--306.
• Computable functors and effective interpretability, M. Harrison-Trainor, A. Melnikov, R. Miller, and A. Montalbán
  J. Symb. Log.,  82  (2017), 77--97.
• Fra\"{\i}ss\'{e}'s conjecture in {$\Pi_1^1$}-comprehension, A. Montalbán
  J. Math. Log.,  17  (2017), 1750006, 12.
• The least Sigma-jump inversion theorem for n-families, M. Faizrahmanov, I. Kalimullin, A. Montalbán, and V. Puzarenko
  J.UCS,  23  (2017), 529--538.
• Sex versus Asex: an analysis of the role of variance conversion, A. E. M. Lewis-Pye and A. Montalbán
  Theoretical Population Biology,  114  (2017), 128--135.
• Degree-invariant, analytic equivalence relations without perfectly many classes, A. Montalbán
  Proc. Amer. Math. Soc.,  145  (2017), 395-398.
• Effectively existentially-atomic structures, A. Montalbán
  Computability and Complexity, Lecture Notes in Computer Science,  10010  (2016), 221-237.
• Classes of structures with no intermediate isomorphism problems, A. Montalbán
  J. Symb. Log.,  81  (2016), 127--150.
• The strength of Turing determinacy within second order arithmetic, A. Montalbán and R. A. Shore
  Fund. Math.,  232  (2016), 249--268.
• The complements of lower cones of degrees and the degree spectra of structures, with Andrews, Cai, Kalimullin, Lempp, and J. Miller
  Journal of Symbolic Logic,  81  (2016), 997--1006.
• Computable structures in generic extensions, J. F. Knight, A. Montalbán, and N. Schweber
  Journal of Symbolic Logic,  81  (2016), 814--832.
• Matemática Computable, A. Montalbán
  Publicaciones Matemáticas del Uruguay,  15  (2016), 1-15.
• Independence in computable algebra, M. Harrison-Trainor, A. Melnikov, and A. Montalbán
  J. Algebra,  443  (2015), 441--468.
• A robuster Scott rank, A. Montalbán
  Proc. Amer. Math. Soc.,  143  (2015), 5427--5436.
• Analytic equivalence relations satisfying hyperarithmetic-is-recursive, A. Montalbán
  Forum Math. Sigma,  3  (2015), e8, 11.
• The complexity of computable categoricity, R. G. Downey, A. M. Kach, S. Lempp, A. E. M. Lewis-Pye, A. Montalbán, and D. D. Turetsky
  Advances in Mathematics,  268  (2015), 423--466.
• Undecidability of the theories of classes of structures, A. Kach and A. Montalbán
  J. Symb. Log.,  79  (2014), 1001--1019.
• Priority arguments via true stages, A. Montalbán
  Journal of Symbolic Logic,  79  (2014), 1315--1335.
• The limits of determinacy in second order arithmetic: consistency and complexity strength, A. Montalbán and R. A. Shore
  Israel J. Math.,  204  (2014), 477--508.
• Computability theoretic classifications for classes of structures, A. Montalbán
  Proceedings of ICM 2014,  2  (2014), 79-101.
• Boolean Algebra Approximations, K. Harris and A. Montalbán
  Transactions of the AMS,  366  (2014), 5223--5256.
• A computability theoretic equivalent to Vaught's conjecture, A. Montalbán
  Advances in Mathematics,  235  (2013), 56--73.
• Extensions of embeddings below computably enumerable degrees, R. Downey, N. Greenberg, A. Lewis, and A. Montalbán
  Transactions of the AMS,  365  (2013), 2977--3018.
• Copyable Structures, A. Montalbán
  Journal of Symbolic Logic,  78  (2013), 1025-1346.
• Relative to any non-hyperarithmetic set, N. Greenberg, A. Montalbán, and T. A. Slaman
  Journal of Mathematical Logic,  13  (2013), .
• A fixed point for the jump operator on structures, A. Montalbán
  Journal of Symbolic Logic,  78  (2013), 425-438.
• Borel structures: a brief survey, A. Montalbán and A. Nies
  Lecture Notes in Logic,  41  (2013), 124-134.
• Isomorphism relations on computable structures, E. B. Fokina, S.-D. Friedman, V. Harizanov, J. F. Knight, C. McCoy, and A. Montalbán
  J. Symbolic Logic,  77  (2012), 122--132.
• Computing Maximal Chains, A. Marcone, A. Montalbán, and R. A. Shore
  Archive for Mathematical Logic,  51  (2012), 651-660.
• Rice Sequences of Relations, A. Montalbán
  Philosophical Transactions of the Royal Society A,  370  (2012), 3464-3487.
• The limits of determinacy in Second Order Arithmetic, A. Montalbán and R. A. Shore
  Proceedings of the London Math Society,  104  (2012), 223-252.
• On the n-Back-and-Forth types of Boolean Algebras, K. Harris and A. Montalbán
  Transactions of the AMS,  364  (2012), 827--866.
• Cuts of linear orders, A. Kach and A. Montalbán
  Order,  28  (2011), 593--600.
• Open questions in Reverse Mathematics, A. Montalbán
  Bulletin of Symbolic Logic,  17  (2011), 431-454.
• Computability of Fraisse limits, B. Csima, V. Harizanov, R. Miller, and A. Montalbán
  Journal of Symbolic Logic,  76  (2011), 66-93.
• The Slaman-Wehner Theorem in higher recursion theory, N. Greenberg, A. Montalbán, and T. A. Slaman
  Proceedings of the AMS,  139  (2011), 1865-1869.
• The Veblen functions for computability theorists, A. Marcone and A. Montalbán
  Journal of Symbolic Logic,  76  (2011), 575--602.
• K-Trivials are never continuously random, G. Barmpalias, N. Greenberg, A. Montalbán, and T. A. Slaman
  Proceedings of the 11th Asian Logic Conference,    (2011), 51-58.
• Counting the back-and-forth types, A. Montalbán
  Journal of Logic and Computability,    (2010), doi: 10.1093/logcom/exq048.
• A Computable aleph_0-categorical Structure Whose Theory Computes True Arithmetic, B. Khoussainov and A. Montalbán
  Journal of Symbolic Logic,  75  (2010), 728-740.
• Notes on the jump of a structure, A. Montalbán
  Mathematical Theory and Computational Practice,    (2009), 372-378.
• On Fraïssé's conjecture for linear orders of finite Hausdorff rank, A. Marcone and A. Montalbán
  Annals of Pure and Applied Logic,  160  (2009), 355-367.
• Embeddings into the Turing degrees, A. Montalbán
  Logic colloquium 2006, Lecture Notes in Logic,    (2009), 229-246.
• From Automatic Structures to Borel Structures, G. Hjorth, B. Khoussainov, A. Montalbán, and A. Nies
  Proceedings of the Twenty-Third Annual IEEE Symposium on Logic in Computer Science (LICS 2008),    (2008), 431-441.
• The isomorphism problem for torsion-free Abelian groups is analytic complete, R. Downey and A. Montalbán
  Journal of Algebra,  320  (2008), 2291-2300.
• Slender classes, R. Downey and A. Montalbán
  Journal of the London Math. Society,  78  (2008), 36-50.
• On the Pi-1-1 Separation Principle, A. Montalbán
  Mathematical Logic Quarterly,  54  (2008), 563-578.
• On the triple jump of the set of atoms of a Boolean algebra, A. Montalbán
  Proceedings of the American Mathematical Society,  136  (2008), 2589-2595.
• Ranked Structures and Arithmetic Transfinite Recursion, N. Greenberg and A. Montalbán
  Transactions of the AMS,  360  (2008), 1265-1307.
• A weakly 2-random set that is not generalized low, A. Lewis, A. Montalbán, and A. Nies
  Proceedings of the CiE 2007,  4497  (2007), 474-477.
• A cappable almost everywhere dominating computably enumerable degree, G. Barmpalias and A. Montalbán
  Proceedings of the Third International Conference on Computability and Complexity in Analysis (CCA 2006),  167  (2007), 17--31 (electronic).
• Subspaces of Computable Vector Spaces, Downey, Hirschfeldt, Kach, Lempp, A. Montalbán, and Mileti.
  Journal of Algebra,  314  (2007), 888-894.
• On the equimorphism types of linear orderings, A. Montalbán
  Bulletin of Symbolic Logic,  13  (2007), 71-99.
• Computable linearizations of well-partial-orderings, A. Montalbán
  Order,  24  (2007), 39-48.
• Countably complementable linear orderings, A. Montalbán
  Order,  23  (2006), 321--331 (2007).
• A minimal pair of K-degrees, B. F. Csima and A. Montalbán
  Proceedings of the American Mathematical Society,  134  (2006), 1499--1502.
• Equivalence between Fraïssé's conjecture and Jullien's theorem, A. Montalbán
  Annals of Pure and Applied Logic,  139  (2006), 1--42.
• There is no ordering on the classes in the generalized high/low hierarchies, A. Montalbán
  Archive for Mathematical Logic,  45  (2006), 215--231.
• Boolean algebras, Tarski invariants, and index sets, B. F. Csima, A. Montalbán, and R. A. Shore
  Notre Dame Journal of Formal Logic,  47  (2006), 1--23.
• Equimorphism invariants for scattered linear orderings, A. Montalbán
  Fundamenta Mathematicae,  191  (2006), 151--173.
• Indecomposable linear orderings and Hyperarithmetic analysis, A. Montalbán
  Journal of Mathematical Logic,  6  (2006), 89-120.
• Teoría de Conjuntos Según Von Newman (Set theory according to von Neuman), A. Montalbán
  Publicaciones Matemáticas del Uruguay,  10  (2005), 91--110.
• Up to equimorphism, hyperarithmetic is recursive, A. Montalbán
  Journal of Symbolic Logic,  70  (2005), 360--378.
• Generalized high degrees have the complementation property, N. Greenberg, A. Montalbán, and R. A. Shore
  Journal of Symbolic Logic,  69  (2004), 1200--1220.
• Embedding jump upper semilattices into the Turing degrees, A. Montalbán
  Journal of Symbolic Logic,  68  (2003), 989--1014.
• Embedding and coding below a 1-generic degree, N. Greenberg and A. Montalbán
  Notre Dame Journal of Formal Logic,  44  (2003), 200--216.