We study the logical structure of Teichm{\"u}ller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness principle from constructive mathematics classically equivalent to the axiom of dependent choice.From there, we state general forms of maximality and well-foundedness principles equivalent to the axiom of choice, including a variant of Zorn's lemma. A comparison with the general class of choice and bar induction principles given by Brede and the first author is initiated.

翻译：我们研究了Teichmüller-Tukey引理（一个等价于选择公理的最大性原则）的逻辑结构，并证明它对应于更新归纳法（一种来自构造性数学的良基原则，在经典数学中等价于相依选择公理）向任意基数的推广。由此，我们陈述了等价于选择公理的最大性与良基原则的一般形式，包括Zorn引理的一个变体。本文还初步比较了由Brede与第一作者给出的选择公理与条形归纳原则的一般分类。