Assuming the Continuum Hypothesis, we interprete the theory of (the cardinal of) continuum with quantification over constructible (monadic, dyadic, etc.) predicates in the monadic (second-order) theory of real line, in the monadic theory of any other short non-modest chain, in the monadic topology of Cantor’s Discontinuum and some other monadic theories. We exhibit monadic sentences defining the real line up to isomorphism under some set-theoretic assumptions. There are some other results.<\/p>\n","protected":false},"excerpt":{"rendered":"
Assuming the Continuum Hypothesis, we interprete the theory of (the cardinal of) continuum with quantification over constructible (monadic, dyadic, etc.) predicates in the monadic (second-order) theory of real line, in the monadic theory of any other short non-modest chain, in the monadic topology of Cantor’s Discontinuum and some other monadic theories. We exhibit monadic sentences 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