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Logic"],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove a topological completeness theorem for the modal logic <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textsf{GLP}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>GLP<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> containing operators <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\{\\langle \\xi \\rangle :\\xi \\in \\textsf{Ord}\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mo>\u27e8<\/mml:mo>\n                    <mml:mi>\u03be<\/mml:mi>\n                    <mml:mo>\u27e9<\/mml:mo>\n                    <mml:mo>:<\/mml:mo>\n                    <mml:mi>\u03be<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mi>Ord<\/mml:mi>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> intended to capture a wellordered sequence of consistency operators increasing in strength. More specifically, we prove that, given a tall-enough scattered space <jats:italic>X<\/jats:italic>, any sentence <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\phi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03d5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> consistent with <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\textsf{GLP}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>GLP<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> can be satisfied on a polytopological space based on finitely many Icard topologies constructed over <jats:italic>X<\/jats:italic> and corresponding to the finitely many modalities that occur in <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\phi $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03d5<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00153-023-00863-9","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T06:32:50Z","timestamp":1677047570000},"page":"751-788","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A topological completeness theorem for transfinite provability logic"],"prefix":"10.1007","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2768-6714","authenticated-orcid":false,"given":"Juan P.","family":"Aguilera","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,2,22]]},"reference":[{"key":"863_CR1","unstructured":"Abashidze, M.: Ordinal completeness of the G\u00f6del-L\u00f6b modal system (in Russian). 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