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arXiv · 2401.00841

Tarski's least fixed point theorem: A predicative type theoretic formulation

Ian Ray
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Abstract

We provide a type theoretic treatment of the paper "On Tarski's fixed point theorem" by Giovanni Curi. There are benefits to having a type theoretic formulation apart from routine implementation in a proof assistant. By taking advantage of (higher) inductive types, we can avoid complicated set theoretic constructions. Arguably, this results in a presentation that is conceptually clearer. Additionally, due the predicative admissibility of (higher) inductive types we take a step towards the "system independent" derivation that Curi calls for in his conclusion. Finally, we explore a condition on monotone maps that guarantees they are `generated' and give an alternative statement of the least fixed point theorem in terms of this condition.

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BibTeXRIS

Ian Ray. 2024-01-01. Tarski's least fixed point theorem: A predicative type theoretic formulation. https://arxiv.org/abs/2401.00841

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