Abstract
We establish the existence of zero elements in certain partially ordered monoids and use them to prove the existence of least fixed points in domain theory. This algebraic stance is the magic underlying Pataraia’s constructive proof of the fixed point theorem.
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Escardo, M.H.: Joins in the frame of nuclei. Applied Categorical Structures 11, 117–124 (2003)
Pataraia, D.: A constructive proof of Tarski’s fixed-point theorem for dcpo’s. Presented in the 65th Peripatetic Seminar on Sheaves and Logic, Aarhus, Denmark (November 1997)
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Martin, K. (2013). Nothing Can Be Fixed. In: Coecke, B., Ong, L., Panangaden, P. (eds) Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science, vol 7860. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38164-5_14
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DOI: https://doi.org/10.1007/978-3-642-38164-5_14
Publisher Name: Springer, Berlin, Heidelberg
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