Sahlqvist theorem for modal fixed point logic

@article{Bezhanishvili2012SahlqvistTF,
  title={Sahlqvist theorem for modal fixed point logic},
  author={Nick Bezhanishvili and Ian M. Hodkinson},
  journal={Theor. Comput. Sci.},
  year={2012},
  volume={424},
  pages={1-19}
}
We define Sahlqvist fixed point formulas. By extending the technique of Sambin and Vaccaro we show that (1) for each Sahlqvist fixed point formula φ there exists an LFP-formula χ(φ), with no free first-order variable or predicate symbol, such that a descriptive μ-frame (an order-topological structure that admits topological interpretations of least fixed point operators as intersections of clopen pre-fixed points) validates φ iff χ(φ) is true in this structure, and (2) every modal fixed point… CONTINUE READING
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