query: Does $K \subseteq L$ and $K \cong L \implies$ $K=L$?
positive_passages.docid: 154318
positive_passages.text: Can a field be isomorphic to its subfield?
negative_passages.docid: 18330
negative_passages.text: Does $R[x] \cong S[x]$ imply $R \cong S$?
negative_passages.docid: 11698
negative_passages.text: $M /K \land L /K$ algebraic $\implies ML/K$ algebraic?
negative_passages.docid: 15276
negative_passages.text: $G \times H \cong G \times K$ , then $ K \cong H$
negative_passages.docid: 120911
negative_passages.text: Clarification on proof: Order of left cosets equal
negative_passages.docid: 80996
negative_passages.text: A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 56399
negative_passages.text: Proof for $A \cup B = B$ if and only if $A \subset B$
negative_passages.docid: 70307
negative_passages.text: $(A\cap B)\cup C = A \cap (B\cup C)$ if and only if $C \subset A$
negative_passages.docid: 31559
negative_passages.text: If $Z\subseteq Y\subseteq X$ and $Z$ is compact in $Y$, then $Z$ is compact in $X$
negative_passages.docid: 66563
negative_passages.text: Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
negative_passages.docid: 144693
negative_passages.text: Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
negative_passages.docid: 16534
negative_passages.text: Can $(\Bbb N,\leq)$ have an $\aleph_0$-categorical theory (in a larger language)?
negative_passages.docid: 147200
negative_passages.text: Given fields $K\subseteq L$, why does $f,g$ relatively prime in $K[x]$ imply relatively prime in $L[x]$?
negative_passages.docid: 79778
negative_passages.text: $\kappa\cdot\kappa= \kappa,$ for infinite cardinals
negative_passages.docid: 80916
negative_passages.text: How to prove that if $A\subseteq A\times A$, then $A=\varnothing$?
negative_passages.docid: 62566
negative_passages.text: Does $X\times S^1\cong Y\times S^1$ imply that $X\times\mathbb R\cong Y\times\mathbb R$?