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• W3088374485 abstract "In this paper, we develop an Isabelle/HOL library of order-theoretic fixed-point theorems. We keep our formalization as general as possible: we reprove several well-known results about complete orders, often with only antisymmetry or attractivity, a mild condition implied by either antisymmetry or transitivity. In particular, we generalize various theorems ensuring the existence of a quasi-fixed point of monotone maps over complete relations, and show that the set of (quasi-)fixed points is itself complete. This result generalizes and strengthens theorems of Knaster-Tarski, Bourbaki-Witt, Kleene, Markowsky, Pataraia, Mashburn, Bhatta-George, and Stouti-Maaden." @default.
• W3088374485 created "2020-10-01" @default.
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• W3088374485 date "2020-09-28" @default.
• W3088374485 modified "2023-09-27" @default.
• W3088374485 title "Fixed Points Theorems for Non-Transitive Relations." @default.
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• W3088374485 hasPublicationYear "2020" @default.
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