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On Tarski's fixed point theorem


Author: Giovanni Curi
Journal: Proc. Amer. Math. Soc. 143 (2015), 4439-4455
MSC (2010): Primary 03G10, 03E70; Secondary 03F65, 18B35
DOI: https://doi.org/10.1090/proc/12569
Published electronically: June 11, 2015
MathSciNet review: 3373943
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Abstract: A notion of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive version of Tarski's fixed point theorem is obtained.


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Giovanni Curi
Affiliation: Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Trieste, 63 - 35121 Padova, Italy
Email: giovanni.curi@email.it

DOI: https://doi.org/10.1090/proc/12569
Keywords: Tarski's fixed point theorem, inductive definitions, constructive set theories, uniform objects
Received by editor(s): March 25, 2013
Received by editor(s) in revised form: November 5, 2013, March 13, 2014, and May 30, 2014
Published electronically: June 11, 2015
Dedicated: To Orsola
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2015 American Mathematical Society