Given a logic \(\mathcal{L}\) specified in this manner, we may now formulate the following problems: \(\sc{SATISFIABILITY}_{\mathcal{L}}\ \) Given a formula \ \phi \in \text{Form}_{\mathcal{L}}\), does there exist a structure \(\mathcal{A} \in \mathfrak{A}\) such that \(\mathcal{A} \models_{\mathcal{L}} \phi\)?
Let be a bounded metric space, and suppose there exists a convexity structure which is compact and -stable.
On the island of Kyushu, there exists a major tectonic structure, known as the Beppu-Shimabara Graben (Matsumoto, 1979), along the northeastern continuation of the Okinawa Trough.
Therefore, it seems probable that within the bundles of collagen fibrils there exists a loose lattice structure.
Within this formalized structure there exists a local cosmology in Samdo as in all Tibetan communities, containing a variety of gods, spirits and ghosts.
At the primary structure level there exists a remarkably high degree of sequence conservation within the TM helices of the PTR family [6,44] (Fig. 1).
By the structure of M, there exists a submodule N⊆ Soc (M), such that M/(N+H ω (M)) is a direct sum of uniserial modules.
He told me about his most recent project: "The question is, does there exist a complex structure on the six-dimensional sphere?
A metric space ( X, d ) is said to have normal (resp. uniform normal) structure if there exists a convexity structure μ on X such that R ( A ) < δ ( A ) (resp. R ( A ) ≤ c ⋅ δ ( A ) for some constant c ∈ ( 0, 1 ) ) for all A ∈ μ which is bounded and consists of more than one point.
A metric space is said to have normal (resp., uniform normal) structure if there exists a convexity structure on such that (resp., for some constant for all which is bounded and consists of more than one point. In this case is said to be normal (resp., uniformly normal) in.
