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Math. Logic"],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We address some phenomena about the interaction between lower semicontinuous submeasures on <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbb {N}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>N<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_{\\sigma }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mi>\u03c3<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> ideals. We analyze the pathology degree of a submeasure and present a method to construct pathological <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_{\\sigma }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mi>\u03c3<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> ideals. We give a partial answers to the question of whether every nonpathological tall <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_{\\sigma }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mi>\u03c3<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> ideal is Kat\u011btov above the random ideal or at least has a Borel selector. Finally, we show a representation of nonpathological <jats:inline-formula><jats:alternatives><jats:tex-math>$$F_{\\sigma }$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>F<\/mml:mi>\n                    <mml:mi>\u03c3<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> ideals using sequences in Banach spaces.\n<\/jats:p>","DOI":"10.1007\/s00153-024-00910-z","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T08:01:51Z","timestamp":1715587311000},"page":"941-967","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Pathology of submeasures and $$F_{\\sigma }$$ ideals"],"prefix":"10.1007","volume":"63","author":[{"given":"Jorge","family":"Mart\u00ednez","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Meza-Alc\u00e1ntara","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carlos","family":"Uzc\u00e1tegui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,5,13]]},"reference":[{"key":"910_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-31557-7","volume-title":"Topics in Banach Space Theory. 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