1.0Microsoft Researchhttps://www.microsoft.com/en-us/researchYuri Gurevichhttps://www.microsoft.com/en-us/research/people/gurevich/Monadic Theory of Order and Topology, I - Microsoft Researchrich600338<blockquote class="wp-embedded-content" data-secret="kH5Xco3ITU"><a href="https://www.microsoft.com/en-us/research/publication/monadic-theory-order-topology/">Monadic Theory of Order and Topology, I</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/publication/monadic-theory-order-topology/embed/#?secret=kH5Xco3ITU" width="600" height="338" title="“Monadic Theory of Order and Topology, I” — Microsoft Research" data-secret="kH5Xco3ITU" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe><script type="text/javascript">
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We disprove two Shelah’s conjectures and prove some more results on the monadic theory of linearly orderings and topological spaces. In particular, if the Continuum Hypothesis holds then there exist monadic formulae expressing the predicates “X is countable” and “X is meager” over the real line and over Cantor’s Discontinuum.