query: Are there really open axioms?
positive_passages.docid: 142840
positive_passages.text: Open axioms of equality
negative_passages.docid: 40291
negative_passages.text: What's the point of the axiom of extensionality?
negative_passages.docid: 3902
negative_passages.text: Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice?
negative_passages.docid: 132287
negative_passages.text: Axiom of Choice and Right Inverse
negative_passages.docid: 139678
negative_passages.text: Advantage of accepting the axiom of choice
negative_passages.docid: 84562
negative_passages.text: Proof using only field axioms
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 12539
negative_passages.text: Set Theory: Equivalency of Axiom of Choice and Choice Function
negative_passages.docid: 33563
negative_passages.text: Is the axiom of choice used in the proof that every open set is the union of basis elements (Mukres, Lemma 13.1)
negative_passages.docid: 126713
negative_passages.text: Strong induction and vacuous truth
negative_passages.docid: 121847
negative_passages.text: Don't we need the axiom of choice to choose from a non-empty set?
negative_passages.docid: 63963
negative_passages.text: deductive system where the axioms are all the propositions that are not tautology
negative_passages.docid: 142219
negative_passages.text: Does the splitting lemma hold without the axiom of choice?
negative_passages.docid: 29744
negative_passages.text: Compactness and axiomatisability
negative_passages.docid: 152976
negative_passages.text: Real Analysis: open and closed sets
negative_passages.docid: 59820
negative_passages.text: ZF Extensionality axiom
negative_passages.docid: 45623
negative_passages.text: Axiom of Choice: What exactly is a choice, and when and why is it needed?