# Large cardinal axioms and independence: The continuum problem revisited

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Let X be an interval, Y a metric space, T a set of parameters, and f : T x X â†’ Y a function. For given t âˆˆ T denote by v(t) the total variation of f(t, â‹…) on X. We look for sufficient conditions for regular (measurable, continuous, etc.) dependence of v on t.

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We study the isomorphism types of ordered structures of concepts for computable formal contexts from the point of view of computable model theory. We show that, although these structures could have the cardinality of the continuum orâ€”if they are countableâ€”could have an arbitrary...