Abstract
We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic IL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{IL}$$\\end{document}. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point property and the Craig interpolation property.
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