@article(brattka, author = "Vasco Brattka", year = "2005", title = "Effective Borel measurability and reducibility of functions", journal = "Mathematical Logic Quarterly", volume = "51", number = "1", pages = "19--44", doi = "10.1002/malq.200310125", ) @article(paulybrattka, author = "Vasco Brattka and Matthew de Brecht and Arno Pauly", year = "2012", title = "Closed Choice and a Uniform Low Basis Theorem", journal = "Annals of Pure and Applied Logic", volume = "163", number = "8", pages = "968--1008", doi = "10.1016/j.apal.2011.12.020", ) @article(brattka3, author = "Vasco Brattka and Guido Gherardi", year = "2011", title = "Effective Choice and Boundedness Principles in Computable Analysis", journal = "Bulletin of Symbolic Logic", volume = "1", pages = "73 -- 117", doi = "10.2178/bsl/1294186663", ) @article(brattka2, author = "Vasco Brattka and Guido Gherardi", year = "2011", title = "Weihrauch Degrees, Omniscience Principles and Weak Computability", journal = "Journal of Symbolic Logic", volume = "76", pages = "143 -- 176", doi = "10.2178/jsl/1294170993", ) @article(gherardi4, author = "Vasco Brattka and Guido Gherardi and Alberto Marcone", year = "2012", title = "The {B}olzano-{W}eierstrass {T}heorem is the Jump of {W}eak {K}\"onig's {L}emma", journal = "Annals of Pure and Applied Logic", volume = "163", number = "6", pages = "623--625", doi = "10.1016/j.apal.2011.10.006", ) @inproceedings(paulybrattka2, author = "Vasco Brattka and Arno Pauly", year = "2010", title = "Computation with Advice", editor = "Xizhong Zheng and Ning Zhong", booktitle = "Proceedings Seventh International Conference on Computability and Complexity in Analysis", series = "Electronic Proceedings in Theoretical Computer Science", volume = "24", pages = "41--55", doi = "10.4204/EPTCS.24.9", ) @inproceedings(debrecht4, author = "Matthew de Brecht and Akihiro Yamamoto", year = "2009", title = "$\Sigma ^0_\alpha $-Admissible Representations (Extended Abstract)", editor = "Andrej Bauer and Peter Hertling and Ker-I Ko", booktitle = "Sixth International Conference on Computability and Complexity in Analysis, CCA 2009, August 18-22, 2009, Ljubljana, Slovenia", series = "Open Access Series in Informatics", volume = "11", publisher = "Schloss Dagstuhl", pages = "119--130", doi = "10.4230/OASIcs.CCA.2009.2264", ) @article(hoyrup, author = "Stefano Galatolo and Mathieu Hoyrup and Christobal Robas", year = "2011", title = "Dynamics and abstract computability: computing invariant measures", journal = "Discrete and Continuous Dynamical Systems", volume = "29", number = "1", pages = "193--212", doi = "10.3934/dcds.2011.29.193", ) @article(gherardi, author = "Guido Gherardi and Alberto Marcone", year = "2009", title = "How incomputable is the separable {H}ahn-{B}anach theorem?", journal = "Notre Dame Journal of Formal Logic", volume = "50", number = "4", pages = "393--425", doi = "10.1215/00294527-2009-018", ) @article(hamkins, author = "Joel David Hamkins and Andy Lewis", year = "2000", title = "Infinite Time Turing Machines", journal = "Journal of Symbolic Logic", volume = "65", number = "2", pages = "567--604", doi = "10.2307/2586556", ) @misc(kihara3, author = "Kojiro Higuchi and Takayuki Kihara", title = "Inside the Muchnik Degrees: Discontinuity, Learnability, and Constructivism", howpublished = "preprint", ) @article(paulykojiro, author = "Kojiro Higuchi and Arno Pauly", year = "2013", title = "The degree-structure of {W}eihrauch-reducibility", journal = "Logical Methods in Computer Science", volume = "9", number = "2", doi = "10.2168/LMCS-9(2:2)2013", ) @article(jaynerogers2, author = "J. E. Jayne and C. A. Rogers", year = "1984", title = "Piece-wise closed functions", journal = "Mathematische Annalen", volume = "255", pages = "499--518", doi = "10.1007/BF01451930", ) @article(jaynerogers, author = "J.E. Jayne and C.A. Rogers", year = "1982", title = "First level Borel functions and isomorphisms", journal = "Journal de Math\'{e}matiques Pures et Appliqu\'{e}es", volume = "61", pages = "177--205", ) @article(ros2, author = "Miroslav Ka\v {c}ena and Luca Motto Ros and Brian Semmes", year = "2012", title = "Some observations on 'A New Proof of a Theorem of {J}ayne and {R}ogers'", journal = "Real Analysis Exchange", volume = "38", number = "1", pages = "121--132", ) @book(kechris, author = "Alexander S. Kechris", year = "1995", title = "Classical Descriptive Set Theory", series = "Graduate Texts in Mathematics", volume = "156", publisher = "Springer", doi = "10.1007/978-1-4612-4190-4", ) @article(motto-ros3, author = "Luca Motto Ros", year = "2011", title = "Game representations of classes of piecewise definable functions", journal = "Mathematical Logic Quarterly", volume = "57", number = "1", pages = "95--112", doi = "10.1002/malq.200910124", ) @article(ros, author = "Luca Motto Ros and Brian Semmes", year = "2009", title = "A New Proof of a Theorem of {J}ayne and {R}ogers", journal = "Real Analysis Exchange", volume = "35", number = "1", pages = "195--204", ) @misc(paulyoracletypetwo, author = "Arno Pauly", year = "2009", title = "Infinite Oracle Queries in Type-2 Machines (Extended Abstract)", howpublished = "arXiv:0907.3230v1", ) @article(paulyincomputabilitynashequilibria, author = "Arno Pauly", year = "2010", title = "How Incomputable is Finding {N}ash Equilibria?", journal = "Journal of Universal Computer Science", volume = "16", number = "18", pages = "2686--2710", doi = "10.3217/jucs-016-18-2686", ) @article(paulyreducibilitylattice, author = "Arno Pauly", year = "2010", title = "On the (semi)lattices induced by continuous reducibilities", journal = "Mathematical Logic Quarterly", volume = "56", number = "5", pages = "488--502", doi = "10.1002/malq.200910104", ) @misc(pauly-synthetic-arxiv, author = "Arno Pauly", year = "2012", title = "Compactness and Separation for Represented Spaces", howpublished = "http://arxiv.org/abs/1204.3763", ) @phdthesis(paulyphd, author = "Arno Pauly", year = "2012", title = "Computable Metamathematics and its Application to Game Theory", school = "University of Cambridge", ) @misc(rettinger, author = "Robert Rettinger", year = "2011", title = "Compactness and the Effectivity of Uniformization", howpublished = "Talk at CCA 2011", ) @article(schroder, author = "Matthias Schr\"{o}der", year = "2002", title = "Extended admissibility", journal = "Theoretical Computer Science", volume = "284", number = "2", pages = "519--538", doi = "10.1016/S0304-3975(01)00109-8", ) @phdthesis(semmes, author = "Brian Semmes", year = "2009", title = "A Game for the {B}orel Functions", school = "University of Amsterdam", ) @article(solecki, author = "S. Solecki", year = "1998", title = "Decomposing Borel sets and functions and the structure of Baire class 1 functions", journal = "Journal of the American Mathematical Society", volume = "11", number = "3", pages = "521--550", doi = "10.1090/S0894-0347-98-00269-0", ) @article(tavana, author = "Nazanin Tavana and Klaus Weihrauch", year = "2011", title = "Turing machines on represented sets, a model of computation for analysis", journal = "Logical Methods in Computer Science", volume = "7", pages = "1--21", doi = "10.2168/LMCS-7(2:19)2011", ) @article(Wadge, author = "William W. Wadge", year = "1972", title = "Degrees of complexity of subsets of the {B}aire space", journal = "Notices of the American Mathematical Society", pages = "714--715", ) @techreport(weihrauchb, author = "Klaus Weihrauch", year = "1992", title = "The degrees of discontinuity of some translators between representations of the real numbers", type = "Informatik Berichte", number = "129", institution = "FernUniversit\"at Hagen", address = "Hagen", ) @techreport(weihrauchc, author = "Klaus Weihrauch", year = "1992", title = "The {TTE}-interpretation of three hierarchies of omniscience principles", type = "Informatik Berichte", number = "130", institution = "FernUniversit\"at Hagen", address = "Hagen", ) @book(weihrauchd, author = "Klaus Weihrauch", year = "2000", title = "Computable Analysis. An Introduction", series = "Texts in Theoretical Computer Science", publisher = "Springer-Verlag", doi = "10.1007/978-3-642-56999-9", ) @inproceedings(ziegler7, author = "Martin Ziegler", year = "2005", title = "Computability and continuity on the real arithmetic hierarchy and the power of type-2 nondeterminism", editor = "Barry S. Cooper and Benedikt L\"owe and Leen Torenvliet", booktitle = "New Computational Paradigms, First Conference on Computability in Europe, CiE 2005, Amsterdam, The Netherlands, June 8-12, 2005, Proceedings", series = "Lecture Notes in Computer Science", volume = "3526", publisher = "Springer", pages = "562--571", doi = "10.1007/11494645\_68", ) @article(ziegler2, author = "Martin Ziegler", year = "2007", title = "Real Hypercomputation and Continuity", journal = "Theory of Computing Systems", volume = "41", pages = "177 -- 206", doi = "10.1007/s00224-006-1343-6", ) @article(ziegler3, author = "Martin Ziegler", year = "2007", title = "Revising Type-2 Computation and Degrees of Discontinuity", journal = "Electronic Notes in Theoretical Computer Science", volume = "167", pages = "255--274", doi = "10.1016/j.entcs.2006.08.015", )