query: Zorn's Lemma - partial order, or preorder?
positive_passages.docid: 154759
positive_passages.text: Kuratowski-Zorn Lemma with pre-order (quasi-order, proset) instead poset?
negative_passages.docid: 146062
negative_passages.text: A "Cantor-Schroder-Bernstein" theorem for partially-ordered-sets
negative_passages.docid: 122684
negative_passages.text: How do you prove Well-Ordering without Mathematical Induction? (and vice-versa)
negative_passages.docid: 131163
negative_passages.text: There is a well ordering of the class of all finite sequences of ordinals
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 44224
negative_passages.text: Understanding the order() function
negative_passages.docid: 4103
negative_passages.text: Total ordering on complex numbers
negative_passages.docid: 30587
negative_passages.text: Uncountable well ordered set in $Z^-$ theory.
negative_passages.docid: 39880
negative_passages.text: Cardinality of Orderings of $\mathbb{R}$
negative_passages.docid: 69724
negative_passages.text: Is Zorn's lemma necessary to show discontinuous $f\colon {\mathbb R} \to {\mathbb R}$ satisfying $f(x+y) = f(x) + f(y)$?
negative_passages.docid: 149277
negative_passages.text: Does well-ordering of the proper class of cardinal numbers imply choice?
negative_passages.docid: 114550
negative_passages.text: Well-ordering theorem and second-order logic
negative_passages.docid: 115100
negative_passages.text: Operator Ordering Ambiguities
negative_passages.docid: 7214
negative_passages.text: Does linear ordering need the Axiom of Choice?
negative_passages.docid: 125026
negative_passages.text: When does order of partial derivatives matter?
negative_passages.docid: 74377
negative_passages.text: Is the natural order relation on an idempotent semiring total/linear?
negative_passages.docid: 114579
negative_passages.text: Order in conditional statements