query: For finite $\Sigma$, if $\Sigma \vdash A$ then $\Sigma \models A$
positive_passages.docid: 27734
positive_passages.text: Meaning of symbols $\vdash$ and $ \models$
negative_passages.docid: 155621
negative_passages.text: Finiteness of the dimension of a normed space and compactness
negative_passages.docid: 47159
negative_passages.text: Wanted: example of an increasing sequence of $\sigma$-fields whose union is not a $\sigma$-field
negative_passages.docid: 97024
negative_passages.text: If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 44480
negative_passages.text: Let $\sigma :\{1,2,3,4,5\} \rightarrow \{1,2,3,4,5\}$ be permutations such that $ \sigma^{-1}(j) \leq \sigma(j)~\forall j, 1 \leq j \leq 5$.
negative_passages.docid: 19294
negative_passages.text: ‎If ‎‎$‎X$ is an infinite-dimensional Banach space and ‎‎$‎‎u‎\in ‎B(X)‎$ ,then $\bigcap_{v\in K(X)}\sigma(u+v) =\cdots$
negative_passages.docid: 146006
negative_passages.text: Uncountable $\sigma$-algebra
negative_passages.docid: 117185
negative_passages.text: The union of a strictly increasing sequence of $\sigma$-algebras is not a $\sigma$-algebra
negative_passages.docid: 103307
negative_passages.text: Generate the smallest $\sigma$-algebra containing a given family of sets
negative_passages.docid: 52301
negative_passages.text: Omitting the hypotheses of finiteness of the measure in Egorov theorem
negative_passages.docid: 153542
negative_passages.text: Fixed Field of $\sigma, \tau$
negative_passages.docid: 115860
negative_passages.text: Is a measure for a sigma algebra determined by its values for a generator of the sigma algebra?
negative_passages.docid: 147486
negative_passages.text: Cartesian product of two $\sigma$-algebras is generally not a $\sigma$-algebra?
negative_passages.docid: 63218
negative_passages.text: Is conditional expectation with respect to two sigma algebra exchangeable?
negative_passages.docid: 45939
negative_passages.text: For which $n≥2$ does there exist $\sigma\in A_n$ with $|\sigma| > n$
negative_passages.docid: 146951
negative_passages.text: Every countably generated sigma algebra is generated by a random variable