query: Do Tarski's Axioms prove all of Euclid's Elements?
positive_passages.docid: 27600
positive_passages.text: Gödel's (in)completeness theorems and the axiomatization of Euclidean geometry
negative_passages.docid: 75007
negative_passages.text: How can I prove this relation between the elementary set theory and the elementary logic?
negative_passages.docid: 83475
negative_passages.text: Prove Or Disprove: tr(AB)=tr(A)*tr(B)
negative_passages.docid: 156235
negative_passages.text: Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?
negative_passages.docid: 134588
negative_passages.text: Seeking a direct proof about nested inclusions
negative_passages.docid: 88736
negative_passages.text: How does the Axiom of Extensionality prove the uniqueness of Specified sets?
negative_passages.docid: 101163
negative_passages.text: Does there exist a universal formula of first-order logic that is satisfiable only by structures with infinite domains?
negative_passages.docid: 94958
negative_passages.text: Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?
negative_passages.docid: 84562
negative_passages.text: Proof using only field axioms
negative_passages.docid: 104771
negative_passages.text: Dedekind's cut and axioms
negative_passages.docid: 140868
negative_passages.text: Axiomatization of $\mathbb{Z}$ via well-ordering of positives.
negative_passages.docid: 144050
negative_passages.text: Is there an infinite number of primes constructed as in Euclid's proof?
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: 43462
negative_passages.text: Disprove $\mathcal{P}(A\Delta B) \setminus \{\emptyset\} = \mathcal{P}(A) \Delta\mathcal{P}(B) $. Is my proof good?
negative_passages.docid: 57868
negative_passages.text: Prove $\tau$ is cofinite on $X$ iff $(X,\tau)$ is $T_1$-space and any infinite subset of $X$ is dense in $(X, \tau)$
negative_passages.docid: 63952
negative_passages.text: Disproving: If $(\Gamma\vdash(\phi\,\lor\psi))$, either $(\Gamma\vdash\phi)$ or $(\Gamma\vdash\psi)$ is true
negative_passages.docid: 49385
negative_passages.text: Proving $\forall x (A\to B) \to(A \to \forall x B):x\notin \mbox{free}(A)$ in a Hilbert system where it is not an axiom