Abstract

We use a (countable support) creature construction to show that consistently d=ℵ1=cov(N)<non(M)<non(N)<cof(N)<2ℵ0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\mathfrak d=\\aleph _1= {{\\mathrm{cov}}}(\\mathcal N)< {{\\mathrm{non}}}(\\mathcal M)< {{\\mathrm{non}}}(\\mathcal N)< {{\\mathrm{cof}}}(\\mathcal N) < 2^{\\aleph _0}. \\end{aligned}$$\\end{document}The same method shows the consistency of d=ℵ1=cov(N)<non(N)<non(M)<cof(N)<2ℵ0.\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\mathfrak d=\\aleph _1= {{\\mathrm{cov}}}(\\mathcal N)< {{\\mathrm{non}}}(\\mathcal N)< {{\\mathrm{non}}}(\\mathcal M)< {{\\mathrm{cof}}}(\\mathcal N) < 2^{\\aleph _0}. \\end{aligned}$$\\end{document}

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