{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:01:17Z","timestamp":1743004877037,"version":"3.40.3"},"publisher-location":"Cham","reference-count":44,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319587400"},{"type":"electronic","value":"9783319587417"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-58741-7_31","type":"book-chapter","created":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T16:59:28Z","timestamp":1494521968000},"page":"327-337","source":"Crossref","is-referenced-by-count":0,"title":["Game Characterizations and Lower Cones in the Weihrauch Degrees"],"prefix":"10.1007","author":[{"given":"Hugo","family":"Nobrega","sequence":"first","affiliation":[]},{"given":"Arno","family":"Pauly","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,12]]},"reference":[{"key":"31_CR1","unstructured":"Andretta, A.: The SLO principle and the Wadge hierarchy. In: Bold, S., L\u00f6we, B., R\u00e4sch, T., van Benthem, J. (eds.) Foundations of the Formal Sciences V: Infinite Games, pp. 1\u201338. College Publications (2007)"},{"key":"31_CR2","doi-asserted-by":"crossref","first-page":"73","DOI":"10.2178\/bsl\/1294186663","volume":"1","author":"V Brattka","year":"2011","unstructured":"Brattka, V., Gherardi, G.: Effective choice and boundedness principles in computable analysis. Bull. Symbolic Log. 1, 73\u2013117 (2011). arXiv:0905.4685","journal-title":"Bull. Symbolic Log."},{"key":"31_CR3","doi-asserted-by":"crossref","first-page":"143","DOI":"10.2178\/jsl\/1294170993","volume":"76","author":"V Brattka","year":"2011","unstructured":"Brattka, V., Gherardi, G.: Weihrauch degrees, omniscience principles and weak computability. J. Symbolic Log. 76, 143\u2013176 (2011). arXiv:0905.4679","journal-title":"J. Symbolic Log."},{"key":"31_CR4","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.ic.2015.03.005","volume":"242","author":"V Brattka","year":"2015","unstructured":"Brattka, V., Gherardi, G., H\u00f6lzl, R.: Probabilistic computability and choice. Inf. Comput. 242, 249\u2013286 (2015). http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0890540115000206 , arXiv:1312.7305","journal-title":"Inf. Comput."},{"issue":"6","key":"31_CR5","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.apal.2011.10.006","volume":"163","author":"V Brattka","year":"2012","unstructured":"Brattka, V., Gherardi, G., Marcone, A.: The Bolzano-Weierstrass theorem is the jump of weak K\u00f6nig\u2019s lemma. Ann. Pure Appl. Log. 163(6), 623\u2013625 (2012)","journal-title":"Ann. Pure Appl. Log."},{"key":"31_CR6","unstructured":"Brattka, V., Pauly, A.: On the algebraic structure of Weihrauch degrees (2016). arXiv 1604.08348, http:\/\/arxiv.org\/abs\/1604.08348"},{"issue":"3","key":"31_CR7","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1016\/j.apal.2012.11.001","volume":"164","author":"M Brecht de","year":"2013","unstructured":"de Brecht, M.: Quasi-Polish spaces. Ann. Pure Appl. Log. 164(3), 354\u2013381 (2013)","journal-title":"Ann. Pure Appl. Log."},{"key":"31_CR8","unstructured":"de Brecht, M.: Levels of discontinuity, limit-computability, and jump operators. In: Brattka, V., Diener, H., Spreen, D. (eds.) Logic, Computation, Hierarchies, pp. 79\u2013108 (2014). de Gruyter, arXiv:1312.0697"},{"issue":"2","key":"31_CR9","doi-asserted-by":"crossref","first-page":"633","DOI":"10.2178\/jsl.7802150","volume":"78","author":"R Carroy","year":"2013","unstructured":"Carroy, R.: A quasi-order on continuous functions. J. Symbolic Log. 78(2), 633\u2013648 (2013)","journal-title":"J. Symbolic Log."},{"issue":"2\u20133","key":"31_CR10","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0165-4896(92)90059-E","volume":"24","author":"D Cenzer","year":"1992","unstructured":"Cenzer, D., Remmel, J.: Recursively presented games and strategies. Math. Soc. Sci. 24(2\u20133), 117\u2013139 (1992)","journal-title":"Math. Soc. Sci."},{"issue":"1","key":"31_CR11","doi-asserted-by":"crossref","first-page":"56","DOI":"10.2307\/2694911","volume":"66","author":"J Duparc","year":"2001","unstructured":"Duparc, J.: Wadge hierarchy and Veblen hierarchy part I: Borel sets of finite rank. J. Symbolic Log. 66(1), 56\u201386 (2001). http:\/\/projecteuclid.org\/euclid.jsl\/1183746360","journal-title":"J. Symbolic Log."},{"key":"31_CR12","doi-asserted-by":"crossref","unstructured":"Gale, D., Stewart, F.M.: Infinite games with perfect information. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games, vol. 2, pp. 245\u2013266. Princeton University Press (1953)","DOI":"10.1515\/9781400881970-014"},{"issue":"4","key":"31_CR13","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1215\/00294527-2009-018","volume":"50","author":"G Gherardi","year":"2009","unstructured":"Gherardi, G., Marcone, A.: How incomputable is the separable Hahn-Banach theorem? Notre Dame J. Formal Log. 50(4), 393\u2013425 (2009)","journal-title":"Notre Dame J. Formal Log."},{"key":"31_CR14","unstructured":"Hertling, P.: Unstetigkeitsgrade von Funktionen in der effektiven Analysis. Ph.D. thesis, Fernuniversit\u00e4t, Gesamthochschule in Hagen (Oktober 1996)"},{"issue":"2","key":"31_CR15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2168\/LMCS-9(2:2)2013","volume":"9","author":"K Higuchi","year":"2013","unstructured":"Higuchi, K., Pauly, A.: The degree-structure of Weihrauch-reducibility. Log. Methods Comput. Sci. 9(2), 1\u201317 (2013)","journal-title":"Log. Methods Comput. Sci."},{"key":"31_CR16","series-title":"Springer Monographs in Mathematics","volume-title":"The Higher Infinite: Large Cardinals in Set Theory from their Beginnings","author":"A Kanamori","year":"2005","unstructured":"Kanamori, A.: The Higher Infinite: Large Cardinals in Set Theory from their Beginnings. Springer Monographs in Mathematics, 2nd edn. Springer, Heidelberg (2005)","edition":"2"},{"key":"31_CR17","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4190-4","volume-title":"Classical Descriptive Set Theory","author":"AS Kechris","year":"1995","unstructured":"Kechris, A.S.: Classical Descriptive Set Theory. Graduate Texts in Mathematics, vol. 156. Springer, Heidelberg (1995)"},{"key":"31_CR18","unstructured":"Kihara, T., Pauly, A.: Point degree spectra of represented spaces (2014). arXiv:1405.6866"},{"key":"31_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1007\/978-3-319-20028-6_25","volume-title":"Evolving Computability","author":"S Le Roux","year":"2015","unstructured":"Le Roux, S., Pauly, A.: Weihrauch degrees of finding equilibria in sequential games. In: Beckmann, A., Mitrana, V., Soskova, M. (eds.) CiE 2015. LNCS, vol. 9136, pp. 246\u2013257. Springer, Cham (2015). doi: 10.1007\/978-3-319-20028-6_25"},{"issue":"2","key":"31_CR20","doi-asserted-by":"crossref","first-page":"363","DOI":"10.2307\/1971035","volume":"102","author":"DA Martin","year":"1975","unstructured":"Martin, D.A.: Borel determinacy. Ann. Math. 102(2), 363\u2013371 (1975)","journal-title":"Ann. Math."},{"key":"31_CR21","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.apal.2010.09.010","volume":"162","author":"YN Moschovakis","year":"2010","unstructured":"Moschovakis, Y.N.: Classical descriptive set theory as a refinement of effective descriptive set theory. Ann. Pure Appl. Log. 162, 243\u2013255 (2010)","journal-title":"Ann. Pure Appl. Log."},{"issue":"1","key":"31_CR22","doi-asserted-by":"crossref","first-page":"27","DOI":"10.2178\/jsl\/1231082301","volume":"74","author":"LM Ros","year":"2009","unstructured":"Ros, L.M.: Borel-amenable reducibilities for sets of reals. J. Symbolic Log. 74(1), 27\u201349 (2009). http:\/\/dx.doi.org\/10.2178\/jsl\/1231082301","journal-title":"J. Symbolic Log."},{"issue":"1","key":"31_CR23","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1002\/malq.200910124","volume":"57","author":"LM Ros","year":"2011","unstructured":"Ros, L.M.: Game representations of classes of piecewise definable functions. Math. Log. Q. 57(1), 95\u2013112 (2011)","journal-title":"Math. Log. Q."},{"issue":"1","key":"31_CR24","doi-asserted-by":"crossref","first-page":"67","DOI":"10.4064\/fm224-1-4","volume":"224","author":"LM Ros","year":"2014","unstructured":"Ros, L.M.: Bad Wadge-like reducibilities on the baire space. Fundam. Math. 224(1), 67\u201395 (2014)","journal-title":"Fundam. Math."},{"key":"31_CR25","unstructured":"Ros, L.M., Schlicht, P., Selivanov, V.: Wadge-like reducibilities on arbitrary quasi-Polish spaces. Mathematical Structures in Computer Science pp. 1\u201350 (2014). http:\/\/journals.cambridge.org\/article_S0960129513000339 , arXiv:1204.5338"},{"key":"31_CR26","unstructured":"Neumann, E., Pauly, A.: A topological view on algebraic computation models (2016). arXiv:1602.08004"},{"key":"31_CR27","unstructured":"Nobrega, H., Pauly, A.: Game characterizations and lower cones in the Weihrauch degrees (2015). arXiv:1511.03693"},{"key":"31_CR28","unstructured":"Pauly, A.: Computable Metamathematics and its Application to Game Theory. Ph.D. thesis, University of Cambridge (2012)"},{"key":"31_CR29","unstructured":"Pauly, A.: The descriptive theory of represented spaces (2014). arXiv:1408.5329"},{"key":"31_CR30","unstructured":"Pauly, A.: Many-one reductions and the category of multivalued functions. Mathematical Structures in Computer Science (2015). arXiv:1102.3151"},{"key":"31_CR31","doi-asserted-by":"crossref","unstructured":"Pauly, A.: On the topological aspects of the theory of represented spaces. Computability 5(2), 159\u2013180 (2016). http:\/\/arxiv.org\/abs\/1204.3763","DOI":"10.3233\/COM-150049"},{"key":"31_CR32","unstructured":"Pauly, A., de Brecht, M.: Towards synthetic descriptive set theory: An instantiation with represented spaces (2013). http:\/\/arxiv.org\/abs\/1307.1850"},{"key":"31_CR33","doi-asserted-by":"crossref","unstructured":"Pauly, A., de Brecht, M.: Descriptive set theory in the category of represented spaces. In: 30th Annual ACM\/IEEE Symposium on Logic in Computer Science (LICS), pp. 438\u2013449 (2015)","DOI":"10.1109\/LICS.2015.48"},{"key":"31_CR34","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4115\/jla.2013.5.7","volume":"5","author":"A Pauly","year":"2013","unstructured":"Pauly, A., Ziegler, M.: Relative computability and uniform continuity of relations. J. Log. Anal. 5, 1\u201339 (2013)","journal-title":"J. Log. Anal."},{"issue":"5","key":"31_CR35","first-page":"1","volume":"54","author":"Y Pequignot","year":"2015","unstructured":"Pequignot, Y.: A Wadge hierarchy for second countable spaces. Arch. Math. Log. 54(5), 1\u201325 (2015). http:\/\/dx.doi.org\/10.1007\/s00153-015-0434-y","journal-title":"Arch. Math. Log."},{"issue":"2","key":"31_CR36","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/S0304-3975(01)00109-8","volume":"284","author":"M Schr\u00f6der","year":"2002","unstructured":"Schr\u00f6der, M.: Extended admissibility. Theoret. Comput. Sci. 284(2), 519\u2013538 (2002)","journal-title":"Theoret. Comput. Sci."},{"key":"31_CR37","unstructured":"Schr\u00f6der, M., Selivanov, V.: Hyperprojective hierarchy of QCB $$_{0}$$ -spaces (2014). arXiv:1404.0297 , http:\/\/arxiv.org\/abs\/1404.0297"},{"issue":"8","key":"31_CR38","first-page":"1","volume":"25","author":"M Schr\u00f6der","year":"2014","unstructured":"Schr\u00f6der, M., Selivanov, V.L.: Some hierarchies of QCB $$_{0}$$ -spaces. Math. Struct. Comput. Sci. 25(8), 1\u201325 (2014). arXiv:1304.1647","journal-title":"Math. Struct. Comput. Sci."},{"key":"31_CR39","unstructured":"Semmes, B.: A game for the Borel functions. Ph.D. thesis, University of Amsterdam (2009)"},{"key":"31_CR40","unstructured":"Wadge, W.W.: Reducibility and determinateness on the Baire space. Ph.D. thesis, University of California, Berkeley (1983)"},{"key":"31_CR41","unstructured":"Weihrauch, K.: The degrees of discontinuity of some translators between representations of the real numbers. Informatik Berichte 129, FernUniversit\u00e4t Hagen, Hagen, July 1992"},{"key":"31_CR42","unstructured":"Weihrauch, K.: The TTE-interpretation of three hierarchies of omniscience principles. Informatik Berichte 130, FernUniversit\u00e4t Hagen, Hagen, September 1992"},{"key":"31_CR43","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56999-9","volume-title":"Computable Analysis","author":"K Weihrauch","year":"2000","unstructured":"Weihrauch, K.: Computable Analysis. Springer, Heidelberg (2000)"},{"key":"31_CR44","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/BFb0069298","volume-title":"Cabal Seminar 76\u201377","author":"R Wesep","year":"1978","unstructured":"Wesep, R.: Wadge degrees and descriptive set theory. In: Kechris, A.S., Moschovakis, Y.N. (eds.) Cabal Seminar 76\u201377. LNM, vol. 689, pp. 151\u2013170. Springer, Heidelberg (1978). doi: 10.1007\/BFb0069298"}],"container-title":["Lecture Notes in Computer Science","Unveiling Dynamics and Complexity"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-58741-7_31","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T13:50:34Z","timestamp":1659016234000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-58741-7_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319587400","9783319587417"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-58741-7_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}