query: Godel's Completeness Theorem
positive_passages.docid: 150451
positive_passages.text: Logic soundness and completeness
negative_passages.docid: 49703
negative_passages.text: Analogue of closed graph theorem
negative_passages.docid: 123002
negative_passages.text: Bartle 6.J. proof completion
negative_passages.docid: 152685
negative_passages.text: Parallel postulate from Playfair's axiom
negative_passages.docid: 43626
negative_passages.text: Open Mapping Theorem: counterexample
negative_passages.docid: 81550
negative_passages.text: Linking two theorems: on algebraic closure and on minimal splitting field
negative_passages.docid: 6113
negative_passages.text: Proof of Strong principle of Induction (T. Tao Analysis I)
negative_passages.docid: 78290
negative_passages.text: Countable axiom of choice: why you can't prove it from just ZF
negative_passages.docid: 114550
negative_passages.text: Well-ordering theorem and second-order logic
negative_passages.docid: 91281
negative_passages.text: Proving the so-called "Well Ordering Principle"
negative_passages.docid: 14849
negative_passages.text: Decidability of a predicate.
negative_passages.docid: 92249
negative_passages.text: Every finite set contains its supremum: proof improvement.
negative_passages.docid: 111122
negative_passages.text: Proof of a theorem in Hilbert's system
negative_passages.docid: 84152
negative_passages.text: Hilbert, Gödel, and "God equations" - a 19th century lesson for 21st century physicists?
negative_passages.docid: 27107
negative_passages.text: intersection of the empty set and vacuous truth
negative_passages.docid: 16796
negative_passages.text: Zermelo-Fraenkel set theory and Hilbert's axioms for geometry
negative_passages.docid: 9158
negative_passages.text: Proving that a propositional theory of any cardinality has an independent set of axioms