# Selected Publications

Effectively Closed Sets (Jeffrey B. Remmel), Perspective in Logic, Cambridge U. Press,
350 pages, to appear.
DRAFT

Generically computable structures (with Wesley Calvert and Valentina Harizanov), submitted.

Computability and Categoricity of Weakly Homogeneous Boolean Algebras and Abelian p-Groups, accepted for Downey Festschrift (with Francis Adams and Selwyn Ng), World Scientific Press.

Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic,
Volume 2: Foundations of Mathematics (Jean Larson, Chris Porter and Jindrich Zapletal), World Scientific Press (2021).

Structure and Randomness in Computability and Set Theory (edited with Chris Porter and Jindrich Zapletal), World Scientific Press (2020), 366 pages.

Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic,
Volume 1: Set Theory(Jean Larson, Chris Porter and Jindrich Zapletal) , World Scientific Press (2020), 209 pages

On the complexity of index sets for finite predicate logic programs which allow function symbols (with V.W. Marek and J.B. Remmel),
J. Logic and Computation 30 (2020), 107-156.

Effective categoricity of automatic equivalence and nested equivalence structures( with Jacob Carson and Jeffrey Remmel), Theory of Computing Systems 64 (2020), 1110-1139.

Logic Programming and Effectively Closed Sets (with V.W. Marek and J.B. Remmel), in \emph{Structure and Randomness in Computability and Set Theory}, World Scientific Press (2020), 197-283.
ABSTRACT, ARTICLE at ArXiv

Computability and differentiability of functions on the Cantor space (with Diego Rojas), CiE 2018, Springer Lecture Notes in Computer Science 10936 (2018), 136-145.

The random members of a $\Pi^0_1$ class (with C. Porter), Theory of Computing Systems, 62 (2018) 1637-1671.
ABSTRACT, ARTICLE at ArXiv

The probability of a computable output from a random oracle (with G. Barmpalias and C. Porter), ACM Transactions on Computational Logic 18 (2017), 15 pp.
ABSTRACT, ARTICLE at ArXiv

Injection structures specified by finite state transducers (with S. Buss, M. Minnes, and J.B. Remmel), in Computability and Complexity (Downey Festschrift, New Zealand, 2016), Springer Lecture Notes in Computer Science, Vol. 10010 (2017), 1-24.
ABSTRACT and ARTICLE

Random numbers as probabilities of machine behaviour (with G. Barmpalias and C. Porter), Theoretical Computer Science, 673 (2017), 1-18.
ABSTRACT, ARTICLE at ArXiv

Computability and Categoricity of Weakly Ultrahomogeneous Structures (with F. Adams), Computability 6 (2017), 365-389.
ABSTRACT, ARTICLE at ArXiv

Index sets for finite normal predicate logic programs with function symbols (with V. Marek and J.B. Remmel), in Logical Foundations of Computer Science (LFCS 2016),Springer Lecture Notes in Computer Science vol. 9537 (2015), 60-75.

Algorithmically random functions and effective capacities (with C. Porter),
Theory and Methods of Computation (TAMC 2015), Springer Lecture Notes in Mathematics 9076 (2015), 22-37.
ABSTRACT, ARTICLE at ArXiv

Computability and categoricity of ultrahomogeneous structures (with F. Adams), in \emph{Language, Life, Limits (Proceedings of CiE 2014 ,Computability in Europe)}, Springer
Lecture Notes in Computer Science 8493 (2014), 1-10.

Sub-computable Bounded Randomness (with S. Buss and J.B. Remmel), Logical Methods in Computer Science 10 (2014).
ABSTRACT, ARTICLE at ArXiv

Two-to-One Structures  (with V. Harizanov and J. Remmel), Journal of Logic and Computation 23 (2013), 1195-1223.
ABSTRACT and ARTICLE

Computability theoretic properties of injection structures  (with V. Harizanov and J. Remmel), Algebra and Logic 53 (2014), 39-69.
ABSTRACT and ARTICLE

Index sets for finite normal predicate logic programs  (with V.W. Marek and J.B. Remmel)
ABSTRACT and E-Print at arxiv

Effective randomness of unions and intersections  (with R. Weber), Theory of Computing Systems 52(2013), 48-64.
ABSTRACT and ARTICLE

A connection between the Cantor-Bendixson derivative and the well-founded semantics of logic programs (with J.B. Remmel), Annals of Mathematics and Artificial Intelligence 65 (2012), 1-24.
ABSTRACT and ARTICLE
First appeared in online proceedings of ISAIM 2008, The Tenth International Symposium on Artificial Intelligence and Mathematics (Fort Lauderdale, 2008), 8 pages.

Computability of countable subshifts in one dimension (with A. Dashti, F. Toska and S. Wyman),  Theory of Computing Systems 51 (2012), 352-371.
ABSTRACT and ARTICLE

Algorithmic capacity and randomness of closed sets  (with Paul Brodhead, F. Toska and S. Wyman) , Logical Methods in Computer Science 6 (2011), 1-16.
ABSTRACT and ARTICLE

$\sigma^0_1$ and $\Pi^0_1$ structures (with V. Harizanov and J.B. Remmel),
Annals of Pure and Applied Logic 162 (2011), 490-503.
ABSTRACT and ARTICLE

A superhigh diamond in the c.e.\ $tt$-degrees (with J. Franklin, Jiang Lu and Guohua Wu),  Arch. Math. Logic 50 (2011), 33-44.
ABSTRACT and ARTICLE

Immunity and non-cupping for closed sets (with T. Kihara, R. Weber and G. Wu), Tbilisi Math. Journal 2 (2009), 77-94
ABSTRACT and ARTICLE

Equivalence Structures and Isomorphisms in the Difference Hierarchy (with G. LaForte and J.B. Remmel), Journal of Symbolic Logic 74 (2009), 535-556.
ABSTRACT and ARTICLE

Effective Categoricity of Abelian p-Groups (with W. Calvert, V. Harizanov and A. Morozov) ,  Annals of Pure and Applied Logic 159 (2009), 187-197.
ABSTRACT and ARTICLE

Special Year in Logic–Model Theory and Computable Model Theory (edited with Valentina Harizanov, David Marker and Carol Wood), Archive for Mathematical Logic 48 (2009), 1-6.
ARTICLE

Space Complexity of Abelian Groups (with R. Downey, J.B. Remmel and Z. Uddin) ,
Archive for Math. Logic 48 (2009), 63-76.
ABSTRACT and ARTICLE

Pseudojumps and Pi-0-1 classes  (with G. Laforte and G. Wu), J. Logic and Computation 19 (2009), 77-87.
ABSTRACT and ARTICLE

$K$-triviality of closed sets and continuous functions (with G. Barmpalias, J. Remmel and R. Weber) Journal of Logic and Computation 19 (2009), 3-16.
ABSTRACT and ARTICLE

Linear orders with distinguished function symbol (with B. Csima and B. Khoussainov), Archive for Mathematical Logic 48 (2009), 115-140.
ABSTRACT and ARTICLE

Computable symbolic dynamics (with S. Ali Dashti and J.L.F. King)
Mathematical Logic Quarterly 54 (2008), 524-533.
ABSTRACT and ARTICLE

Special Year in Logic–Computability and Complexity in Analysis (edited with Rebecca Weber), Archive for Mathematical Logic 45 (2008), 529-531.
ARTICLE

Degrees of difficulty of generalized r.e. separating classes (with Peter Hinman), Archive for Mathematical Logic 45 (2008), 629-647.
ABSTRACT and ARTICLE
First appeared as Medvedev degrees of generalized r.e. separating classes
Proc. CCA 2006, D. Cenzer, R. Dillhage, T. Grubb and Klaus Weihrauch (eds.): Third International Conference on Computability and Complexity in Analysis, Information Berichte, FernUniversit\”{a}t (2006), 125-142, and Springer Electronic Notes in Computer Science 167 (2007), 203-223.

Effectively closed sets and enumerations (with Paul Brodhead) Archive for Mathematical Logic 45 (2008), 565-582.
ABSTRACT and ARTICLE

Algorithmic Randomness of Continuous Functions (with G. Barmpalias, P. Brodhead, J.B. Remmel and R. Weber) Archive for Mathematical Logic 45 (2008), 533-546.
ABSTRACT and ARTICLE

Algorithmic Randomness of Closed Sets (with G. Barmpalias, P. Brodhead and A. S. Dashti and R. Weber) Journal for Logic and Computation, 17 (2007), 1041-1062.
ABSTRACT and ARTICLE

Proceedings CCA 2006, Third International Conference on Computability and Complexity in Analysis, (edited with R. Dillhage, T. Grubb and Klaus Weihrauch)
Information Berichte FernUniversit\”{a}t Hagen (2006), and Springer Electronic Notes in Computer Science 167 (2007).
ARTICLE

On the complexity of inductive definitions (with J. Remmel) Mathematical Structures in Computer Science 16 (2006), 763-788.
ABSTRACT and ARTICLE

Complexity, decidability and completeness (with J. Remmel) Journal of Symbolic Logic 71 (2006), 399-424.
ABSTRACT and ARTICLE

Effective categoricity of Equivalence Structures (with W. Calvert, V. Harizanov and A. Morozov) Annals of Pure and Applied Logic, 141 (2006), 61-78.
ABSTRACT and ARTICLE

Logic programming with infinite sets, (with W. Marek and J. Remmel)
Annals of Artificial Intelligence and Mathematics 44 (2005), 309–339.
ABSTRACT and ARTICLE

Minimal Extensions of Pi-0-1 Classes, (with F. Riazati) Mathematical Logic Quarterly 51 (2005), 206-216.
ABSTRACT
and ARTICLE

Proof-Theoretic Strength of the Stable Marriage Theorem and Other Problems (with J. Remmel) “Reverse Mathematics”, edited by S. Simpson, ASL Lecture Notes in Logic 21, AK Peters (2005), 67–103.
ABSTRACT and ARTICLE

Index sets for computable differential equations, (with J. Remmel)
Mathematical Logic Quarterly 50 (2004), 329-344.
ABSTRACT and ARTICLE

Locally determined logic programs and recursive stable models (with J. Remmel and A. Vanderbilt) Annals of Mathematics and Artificial Intelligence 40 (2004), 225-262.
ABSTRACT and ARTICLE