query: Prove that for an arbitrary (possibly infinite) language, that for a finite L-structure $M$, if $M \equiv N$ then $ M \cong N$
positive_passages.docid: 19604
positive_passages.text: Complete first order theory with finite model is categorical
negative_passages.docid: 150199
negative_passages.text: How to prove for a finite group that $|\langle g \rangle|=o(g)$?
negative_passages.docid: 66398
negative_passages.text: Union of a finite set and a countably infinite set is countably infinite
negative_passages.docid: 49166
negative_passages.text: $R^n \cong R^m$ iff $n=m$
negative_passages.docid: 59566
negative_passages.text: Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
negative_passages.docid: 151928
negative_passages.text: How to prove that $N\setminus A$ is finite?
negative_passages.docid: 85799
negative_passages.text: Finding languages such that $L_{1} \subseteq L_{2} \subseteq L_{3}$ where $L_{1}, L_{3} \notin \mathbb{R}$, $L_{2} \in \mathbb{R}$
negative_passages.docid: 139078
negative_passages.text: Infinite partition of $\mathbb N$ by infinite subsets
negative_passages.docid: 139828
negative_passages.text: Finitely Presented Modules and Exact Sequences
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
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: 103427
negative_passages.text: When is $\operatorname{Hom}_A(M,N)$ finitely generated?
negative_passages.docid: 102113
negative_passages.text: Proof that the number of proofs is countably infinite
negative_passages.docid: 123847
negative_passages.text: Cardinality of $GL_n(K)$ when $K$ is finite
negative_passages.docid: 86926
negative_passages.text: Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
negative_passages.docid: 137646
negative_passages.text: show that language $L'$ is regular (given $L$ regular)
negative_passages.docid: 122828
negative_passages.text: Proof that TREE(n) where n >= 3 is finite?