{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,23]],"date-time":"2025-12-23T12:25:08Z","timestamp":1766492708499},"reference-count":38,"publisher":"Duke University Press","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Notre Dame J. Formal Logic"],"published-print":{"date-parts":[[2018,1,1]]},"DOI":"10.1215\/00294527-2018-0016","type":"journal-article","created":{"date-parts":[[2018,10,13]],"date-time":"2018-10-13T02:01:24Z","timestamp":1539396084000},"source":"Crossref","is-referenced-by-count":5,"title":["On the Uniform Computational Content of the Baire Category Theorem"],"prefix":"10.1215","volume":"59","author":[{"given":"Vasco","family":"Brattka","sequence":"first","affiliation":[]},{"given":"Matthew","family":"Hendtlass","sequence":"additional","affiliation":[]},{"given":"Alexander P.","family":"Kreuzer","sequence":"additional","affiliation":[]}],"member":"73","reference":[{"key":"15","unstructured":"[15] Brattka, V., and A. Pauly, \u201cOn the algebraic structure of Weihrauch degrees,\u201d preprint, <a href=\"arXiv:1604.08348v7\">arXiv:1604.08348v7<\/a> [cs.LO]."},{"key":"36","unstructured":"[36] Weihrauch, K., \u201cThe degrees of discontinuity of some translators between representations of the real numbers,\u201d technical report TR-92-050, International Computer Science Institute, Berkeley, Calif., 1992, <a href=\"http:\/\/www.icsi.berkeley.edu\/pubs\/techreports\/tr-92-050.pdf\">http:\/\/www.icsi.berkeley.edu\/pubs\/techreports\/tr-92-050.pdf<\/a>."},{"key":"1","doi-asserted-by":"publisher","unstructured":"[1] Avigad, J., E. T. Dean, and J. Rute, \u201cAlgorithmic randomness, reverse mathematics, and the dominated convergence theorem,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 163 (2012), pp. 1854\u201364.","DOI":"10.1016\/j.apal.2012.05.010"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] Barmpalias, G., A. R. Day, and A. E. M. Lewis-Pye, \u201cThe typical Turing degree,\u201d <i>Proceedings of the London Mathematical Society (3)<\/i>, vol. 109 (2014), pp. 1\u201339.","DOI":"10.1112\/plms\/pdt065"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] Bienvenu, L., and L. Patey, \u201cDiagonally non-computable functions and fireworks,\u201d <i>Information and Computation<\/i>, vol. 253 (2017), pp. 64\u201377.","DOI":"10.1016\/j.ic.2016.12.008"},{"key":"4","doi-asserted-by":"publisher","unstructured":"[4] Brattka, V., \u201cComputable invariance,\u201d <i>Theoretical Computer Science<\/i>, vol. 210 (1999), pp. 3\u201320.","DOI":"10.1016\/S0304-3975(98)00095-4"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] Brattka, V., \u201cComputable versions of Baire\u2019s category theorem,\u201d pp. 224\u201335 in <i>Mathematical Foundations of Computer Science, 2001(Mari\u00e1nsk\u00e9 L\u00e1zn\u011b)<\/i>, edited by J. Sgall, A. Pultr, and P. Kolman, vol. 2136 of <i>Lecture Notes in Computer Science<\/i>, Springer, Berlin, 2001.","DOI":"10.1007\/3-540-44683-4_20"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] Brattka, V., \u201cEffective Borel measurability and reducibility of functions,\u201d <i>Mathematical Logic Quarterly<\/i>, vol. 51 (2005), pp. 19\u201344.","DOI":"10.1002\/malq.200310125"},{"key":"7","doi-asserted-by":"crossref","unstructured":"[7] Brattka, V., \u201cFrom Hilbert\u2019s 13th problem to the theory of neural networks: constructive aspects of Kolmogorov\u2019s superposition theorem,\u201d pp. 253\u201380 in <i>Kolmogorov\u2019s Heritage in Mathematics<\/i>, edited by \u00c9. Charpentier, A. Lesne, and N. Nikolski, Springer, Berlin, 2007.","DOI":"10.1007\/978-3-540-36351-4_13"},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] Brattka, V., M. de Brecht, and A. Pauly, \u201cClosed choice and a uniform low basis theorem,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 163 (2012), pp. 986\u20131008.","DOI":"10.1016\/j.apal.2011.12.020"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] Brattka, V., and G. Gherardi, \u201cBorel complexity of topological operations on computable metric spaces,\u201d <i>Journal of Logic and Computation<\/i>, vol. 19 (2009), pp. 45\u201376.","DOI":"10.1093\/logcom\/exn027"},{"key":"10","doi-asserted-by":"publisher","unstructured":"[10] Brattka, V., and G. Gherardi, \u201cEffective choice and boundedness principles in computable analysis,\u201d <i>Bulletin of Symbolic Logic<\/i>, vol. 17 (2011), pp. 73\u2013117.","DOI":"10.2178\/bsl\/1294186663"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] Brattka, V., and G. Gherardi, \u201cWeihrauch degrees, omniscience principles and weak computability,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 76 (2011), pp. 143\u201376.","DOI":"10.2178\/jsl\/1294170993"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] Brattka, V., G. Gherardi, and R. H\u00f6lzl, \u201cProbabilistic computability and choice,\u201d <i>Information and Computation<\/i>, vol. 242 (2015), pp. 249\u201386.","DOI":"10.1016\/j.ic.2015.03.005"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] Brattka, V., G. Gherardi, and A. Marcone, \u201cThe Bolzano-Weierstrass theorem is the jump of weak K\u0151nig\u2019s lemma,\u201d <i>Annals of Pure and Applied Logic<\/i>, vol. 163 (2012), pp. 623\u201355.","DOI":"10.1016\/j.apal.2011.10.006"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] Brattka, V., M. Hendtlass, and A. P. Kreuzer, \u201cOn the uniform computational content of computability theory,\u201d <i>Theory of Computing Systems<\/i>, vol. 61 (2017), pp. 1376\u2013426.","DOI":"10.1007\/s00224-017-9798-1"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] Brattka, V., and G. Presser, \u201cComputability on subsets of metric spaces,\u201d <i>Theoretical Computer Science<\/i>, vol. 305 (2003), pp. 43\u201376.","DOI":"10.1016\/S0304-3975(02)00693-X"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] Brown, D. K., and S. G. Simpson, \u201cThe Baire category theorem in weak subsystems of second-order arithmetic,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 58 (1993), pp. 557\u201378.","DOI":"10.2307\/2275219"},{"key":"18","doi-asserted-by":"publisher","unstructured":"[18] Dorais, F. G., D. D. Dzhafarov, J. L. Hirst, J. R. Mileti, and P. Shafer, \u201cOn uniform relationships between combinatorial problems,\u201d <i>Transactions of the American Mathematical Society<\/i>, vol. 368 (2016), pp. 1321\u201359.","DOI":"10.1090\/tran\/6465"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] Downey, R. G., and D. R. Hirschfeldt, <i>Algorithmic Randomness and Complexity<\/i>, Theory and Applications of Computability, Springer, New York, 2010.","DOI":"10.1007\/978-0-387-68441-3"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] Gherardi, G., and A. Marcone, \u201cHow incomputable is the separable Hahn-Banach theorem?,\u201d <i>Notre Dame Journal of Formal Logic<\/i>, vol. 50 (2009), pp. 393\u2013425.","DOI":"10.1215\/00294527-2009-018"},{"key":"21","unstructured":"[21] Hertling, P., \u201cUnstetigkeitsgrade von Funktionen in der effektiven Analysis,\u201d Ph.D. dissertation, Fernuniversit\u00e4t Hagen, Hagen, 1996."},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] Hirschfeldt, D. R., <i>Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles<\/i>, vol. 28 of <i>Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore<\/i>, World Scientific, Singapore, 2015.","DOI":"10.1017\/bsl.2015.18"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] Hirschfeldt, D. R., R. A. Shore, and T. A. Slaman, \u201cThe atomic model theorem and type omitting,\u201d <i>Transactions of the American Mathematical Society<\/i>, vol. 361 (2009), pp. 5805\u201337.","DOI":"10.1090\/S0002-9947-09-04847-8"},{"key":"24","doi-asserted-by":"crossref","unstructured":"[24] Ku\u010dera, A., \u201cMeasure, $\\Pi^{0}_{1}$-classes and complete extensions of $\\mathrm{PA}$,\u201d pp. 245\u201359 in <i>Recursion Theory Week (Oberwolfach, 1984)<\/i>, vol. 1141 of <i>Lecture Notes in Mathematics<\/i>, Springer, Berlin, 1985.","DOI":"10.1007\/BFb0076224"},{"key":"25","unstructured":"[25] Kurtz, S. A., \u201cRandomness and genericity in the degrees of unsolvability,\u201d Ph.D. dissertation, University of Illinois at Urbana\u2013Champaign, Urbana, Ill., 1981."},{"key":"26","unstructured":"[26] Miller, J. S., \u201cPi-0-1 classes in computable analysis and topology,\u201d Ph.D. dissertation, Cornell University, Ithaca, N.Y., 2002."},{"key":"27","doi-asserted-by":"crossref","unstructured":"[27] Nies, A., <i>Computability and Randomness<\/i>, vol. 51 of <i>Oxford Logic Guides<\/i>, Oxford University Press, New York, 2009.","DOI":"10.1093\/acprof:oso\/9780199230761.003.0009"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[28] Nies, A., F. Stephan, and S. A. Terwijn, \u201cRandomness, relativization and Turing degrees,\u201d <i>Journal of Symbolic Logic<\/i>, vol. 70 (2005), pp. 515\u201335.","DOI":"10.2178\/jsl\/1120224726"},{"key":"29","unstructured":"[29] Pauly, A., \u201cHow incomputable is finding Nash equilibria?,\u201d <i>Journal of Universal Computer Science<\/i>, vol. 16 (2010), pp. 2686\u2013710."},{"key":"30","doi-asserted-by":"publisher","unstructured":"[30] Pauly, A., \u201cOn the (semi)lattices induced by continuous reducibilities,\u201d <i>Mathematical Logic Quarterly<\/i>, vol. 56 (2010), pp. 488\u2013502.","DOI":"10.1002\/malq.200910104"},{"key":"31","doi-asserted-by":"crossref","unstructured":"[31] Rumyantsev, A., and A. Shen, \u201cProbabilistic constructions of computable objects and a computable version of Lov\u00e1sz local lemma,\u201d <i>Fundamenta Informaticae<\/i>, vol. 132 (2014), pp. 1\u201314.","DOI":"10.3233\/FI-2014-1029"},{"key":"32","unstructured":"[32] Schr\u00f6der, M., \u201cAdmissible representations for continuous computations,\u201d Ph.D. dissertation, Fernuniversit\u00e4t Hagen, Hagen, 2002."},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] Simpson, S. G., \u201cBaire categoricity and $\\Sigma^{0}_{1}$-induction,\u201d <i>Notre Dame Journal of Formal Logic<\/i>, vol. 55 (2014), pp. 75\u201378.","DOI":"10.1215\/00294527-2377887"},{"key":"34","unstructured":"[34] Stein, T. V., \u201cVergleich nicht konstruktiv l\u00f6sbarer Probleme in der Analysis,\u201d Ph.D. dissertation, Fernuniversit\u00e4t Hagen, Hagen, 1989."},{"key":"35","doi-asserted-by":"crossref","unstructured":"[35] Tavana, N. R., and K. Weihrauch, \u201cTuring machines on represented sets, a model of computation for analysis,\u201d <i>Logical Methods in Computer Science<\/i>, vol. 7 (2011), no. 2:19.","DOI":"10.2168\/LMCS-7(2:19)2011"},{"key":"37","unstructured":"[37] Weihrauch, K., \u201cThe TTE-interpretation of three hierarchies of omniscience principles,\u201d Informatik Berichte 130, Fernuniversit\u00e4t Hagen, Hagen, 1992."},{"key":"38","doi-asserted-by":"crossref","unstructured":"[38] Weihrauch, K., <i>Computable Analysis<\/i>, Springer, Berlin, 2000.","DOI":"10.1007\/978-3-642-56999-9"}],"container-title":["Notre Dame Journal of Formal Logic"],"original-title":[],"link":[{"URL":"https:\/\/projecteuclid.org\/journalArticle\/Download?urlid=10.1215\/00294527-2018-0016","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,30]],"date-time":"2024-01-30T20:59:36Z","timestamp":1706648376000},"score":1,"resource":{"primary":{"URL":"https:\/\/projecteuclid.org\/journals\/notre-dame-journal-of-formal-logic\/volume-59\/issue-4\/On-the-Uniform-Computational-Content-of-the-Baire-Category-Theorem\/10.1215\/00294527-2018-0016.full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1,1]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,1,1]]}},"URL":"https:\/\/doi.org\/10.1215\/00294527-2018-0016","relation":{},"ISSN":["0029-4527"],"issn-type":[{"value":"0029-4527","type":"print"}],"subject":[],"published":{"date-parts":[[2018,1,1]]}}}