{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:23:11Z","timestamp":1740108191506,"version":"3.37.3"},"reference-count":6,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T00:00:00Z","timestamp":1686268800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper is concerned with the proper way to effectivize the notion of a Polish space. A theorem is proved that shows the recursive Polish space structure is not found in the effectively open subsets of a space <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathcal {X}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>X<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and we explore strong evidence that the effective structure is instead captured by the effectively open subsets of the product space <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathbb {N}\\times {\\mathcal {X}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>N<\/mml:mi>\n                    <mml:mo>\u00d7<\/mml:mo>\n                    <mml:mi>X<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.\n<\/jats:p>","DOI":"10.1007\/s00153-023-00883-5","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T16:01:44Z","timestamp":1686326504000},"page":"1101-1110","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Recursive Polish spaces"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2173-1390","authenticated-orcid":false,"given":"Tyler","family":"Arant","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,9]]},"reference":[{"key":"883_CR1","doi-asserted-by":"publisher","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. Spinger, New York (1995)"},{"key":"883_CR2","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/155","volume-title":"Descriptive Set Theory","author":"YN Moschovakis","year":"2009","unstructured":"Moschovakis, Y.N.: Descriptive Set Theory. American Mathematical Society, Providence (2009)"},{"key":"883_CR3","unstructured":"Arant, T., Gregoriades, V., Moschovakis, Y.N.: Notes on Effective Descriptive Set Theory (to appear)"},{"key":"883_CR4","volume-title":"Theory of Recursive Functions and Effective Computability","author":"H Rogers","year":"1987","unstructured":"Rogers, H.: Theory of Recursive Functions and Effective Computability. MIT Press, Cambridge (1987)"},{"key":"883_CR5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69965-8","volume-title":"Computability","author":"K Weihrauch","year":"1987","unstructured":"Weihrauch, K.: Computability. Springer, New York (1987)"},{"key":"883_CR6","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1017\/S0960129516000128","volume":"27","author":"V Gregoriades","year":"2016","unstructured":"Gregoriades, V., Kisp\u00e9ter, T., Pauly, A.: A comparison of concepts from computable analysis and effective descriptive set theory. Math. Struct. Comput. Sci. 27, 1414\u20131436 (2016)","journal-title":"Math. Struct. Comput. Sci."}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-023-00883-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-023-00883-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-023-00883-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,20]],"date-time":"2023-09-20T03:27:58Z","timestamp":1695180478000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-023-00883-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,9]]},"references-count":6,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["883"],"URL":"https:\/\/doi.org\/10.1007\/s00153-023-00883-5","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2023,6,9]]},"assertion":[{"value":"6 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}