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In particular we show that, given a finite number of \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\Delta ^{1}_{1}$\\end{document}<\/jats:styled-content> equivalence relations \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrel {\\mathsf {F}}_1,\\dots ,\\mathrel {\\mathsf {F}}_n$\\end{document}<\/jats:styled-content>, any \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\Sigma ^{1}_{1}$\\end{document}<\/jats:styled-content> set A<\/jats:italic> of the Baire space either is covered by compact \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\Delta ^{1}_{1}$\\end{document}<\/jats:styled-content> sets and lightface \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\Delta ^{1}_{1}$\\end{document}<\/jats:styled-content> equivalence classes of the relations \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrel {\\mathsf {F}}_i$\\end{document}<\/jats:styled-content>, or A<\/jats:italic> contains a superperfect subset which is pairwise \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrel {\\mathsf {F}}_i$\\end{document}<\/jats:styled-content>\u2010inequivalent for all i<\/jats:italic> = 1, \u2026, n<\/jats:italic>. Further generalizations to \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\Sigma ^{1}_{2}$\\end{document}<\/jats:styled-content> sets A<\/jats:italic> are obtained.<\/jats:p>","DOI":"10.1002\/malq.201200001","type":"journal-article","created":{"date-parts":[[2013,4,16]],"date-time":"2013-04-16T07:36:58Z","timestamp":1366097818000},"page":"147-166","source":"Crossref","is-referenced-by-count":3,"title":["On effective \u03c3\u2010boundedness and \u03c3\u2010compactness"],"prefix":"10.1002","volume":"59","author":[{"given":"Vladimir","family":"Kanovei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vassily","family":"Lyubetsky","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2013,4,16]]},"reference":[{"key":"e_1_2_14_2_1","article-title":"Borel liftings of Borel sets: some decidable and undecidable statements","volume":"876","author":"Debs G.","year":"2007","journal-title":"Mem. 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