TL;DR
This paper introduces an abstract inductive definition on complete lattices and uses it to develop a constructive, predicative version of Tarski's fixed point theorem, expanding its foundational understanding.
Contribution
It formulates a new concept of abstract inductive definition and derives a constructive, predicative version of Tarski's fixed point theorem.
Findings
Established a new abstract inductive framework
Derived a constructive version of Tarski's fixed point theorem
Enhanced foundational understanding of fixed point theory
Abstract
A concept of abstract inductive definition on a complete lattice is formulated and studied. As an application, a constructive and predicative version of Tarski's fixed point theorem is obtained.
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Taxonomy
TopicsAdvanced Algebra and Logic · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra