Sur le théorème de Zorn

  title={Sur le th{\'e}or{\`e}me de Zorn},
  author={N. Bourbaki},
  journal={Archiv der Mathematik},
  • N. Bourbaki
  • Published 1949
  • Mathematics
  • Archiv der Mathematik
Agreement theorems in dynamic-epistemic logic
It is shown that common belief of posteriors is sufficient for agreements in "epistemic-plausibility models", under common and well-founded priors, from which the usual form of agreement results follows, using common knowledge. Expand
Reverse Mathematics and Countable Algebraic Systems
This thesis is a contribution to the foundation of mathematics, especially to the Reverse Mathematics program, whose core question is “What are the appropriate axioms to prove each mathematicalExpand
Maximal and Variational Principles in Vector Spaces
In Sect. 1, a separable type extension of Ekeland’s variational principle (J Math Anal Appl 47:324–353, 1974) is given, in the realm of ordered convergence spaces. The connections with a relatedExpand
Ultrametric fixed points in reduced axiomatic systems
The Brezis-Browder ordering principle [Advances Math., 21 (1976), 355-364] is used to get a proof, in the reduced axiomatic system (ZF-AC+DC), of a fixed point result [in the complete axiomaticExpand
New equivalents of the axiom of choice and consequences
This paper continues the study of the Axiom of Choice by E. Z e r m e l o [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107–128; translated in van Heijenoort 1967,Expand
A fixed point conversion is given for the pseudometric variational principle in Tataru (18). The obtained facts are then used to get an improved version of the fixed point result in Ray and WalkerExpand
A Mechanized Proof of the Max-Flow Min-Cut Theorem for Countable Networks
This paper formalizes the max-flow min-cut theorem for countable networks proof in Isabelle/HOL and provides a simpler proof for networks where the total outgoing capacity of all vertices other than the source is finite. Expand
An Initial Algebra Theorem Without Iteration
A constructive proof of the Initial Algebra Theorem that avoids transfinite iteration of the functor and equivalently obtain convergence of the initial-algebra chain as an equivalent condition, overall yielding a streamlined version of the original proof. Expand
A note on the Knaster–Tarski Fixpoint Theorem
This note shows that several statements about fixpoints in order theory are equivalent to Knaster–Tarski Fixpoint Theorem for complete lattices. All proofs have been done in Zermelo–Fraenkel setExpand