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A note on the Knaster–Tarski Fixpoint Theorem

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Abstract

This note shows that several statements about fixpoints in order theory are equivalent to Knaster–Tarski Fixpoint Theorem for complete lattices. All proofs have been done in Zermelo–Fraenkel set theory without the Axiom of Choice.

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Acknowledgements

Authors are grateful to the anonymous referees for their insightful suggestions which are very detailed and extremely helpful in improving the presentation of this paper.

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Correspondence to Mengqiao Huang.

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Presented by R. Pöschel.

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This research is supported by “Double-first-class” Applied Characteristic Construction Discipline (Applied Economics) in Hunan Province (Grant no. Xiangjiaotong [2018] 469), and supported by NSF of China 61772336.

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Huang, M., Fu, Y. A note on the Knaster–Tarski Fixpoint Theorem. Algebra Univers. 81, 47 (2020). https://doi.org/10.1007/s00012-020-00676-4

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  • DOI: https://doi.org/10.1007/s00012-020-00676-4

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