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  "body": "\n## Statement\n\nIn mathematical logic and computer science, **Kamp's theorem** states that linear temporal logic is equivalent to the monadic first-order logic of order over the [[non-negative integers|0MWKJ44V5A]] and the [[real numbers|08J2M1JYAG]]. It is the oldest result in expressive completeness, the study of determining if a given logic can express a desired subject matter. In temporal logic, a logic $\\mathcal L$ is expressive complete if every first-order formula with one free variable is equivalent to a formula in $\\mathcal L$. The theorem was proven by Hans Kamp in his doctoral thesis, *Tense Logic and the Theory of Linear Order* (1968). In this thesis, Kamp introduces the $\\mathbf U$ and $\\mathbf S$ operators to Prior's tense logic, increasing its expressive power and ensuring expressive completeness. Explicitly, Kamp shows that the $\\mathbf X, \\mathbf Y, \\mathbf F, \\mathbf P$ operators cannot express $\\mathbf U$.\n",
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