query: Ordered Fields and the Completeness Axiom
positive_passages.docid: 158081
positive_passages.text: Is the IVT equivalent to completeness?
negative_passages.docid: 104550
negative_passages.text: Countable union of countable sets(ZF)
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 79725
negative_passages.text: Fields of arbitrary cardinality
negative_passages.docid: 82169
negative_passages.text: Why does a partially ordered set need to be reflexive?
negative_passages.docid: 74377
negative_passages.text: Is the natural order relation on an idempotent semiring total/linear?
negative_passages.docid: 69337
negative_passages.text: Zorn's Lemma And Axiom of Choice
negative_passages.docid: 62936
negative_passages.text: Proving equivalencies of two versions of the Axiom of Choice
negative_passages.docid: 17
negative_passages.text: First Order Language for vector spaces over fields
negative_passages.docid: 123419
negative_passages.text: Abstract algebra: homomorphism and an element of a prime order
negative_passages.docid: 82009
negative_passages.text: Prove that every totally ordered set has a well-ordered cofinal subset
negative_passages.docid: 118617
negative_passages.text: Completeness and Incompleteness
negative_passages.docid: 131163
negative_passages.text: There is a well ordering of the class of all finite sequences of ordinals
negative_passages.docid: 31722
negative_passages.text: Prove $-(-a)=a$ using only ordered field axioms
negative_passages.docid: 81423
negative_passages.text: Completeness and Topological Equivalence
negative_passages.docid: 121732
negative_passages.text: Functional completeness of $\{\text{or},\text{ xor}, \text{ xnor}\}$
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability