We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than ω.

We prove that the theory of open projective planes is complete and strictly stable, infer from this Marshall Hall's free ( π n : 4 ⩽ ω ) are all elementary equivalent their common stable decidable, being in fact planes. further characterize substructure relation class planes, show particular an chain. then does not have a prime model, it has elimination quantifiers down to Boolean combinations ...

Derivative-free iterative methods are useful to approximate the numerical solutions when given function lacks explicit derivative information or derivatives too expensive compute. Exploring convergence properties of such is crucial in their development. The behavior approaches and determining practical applicability require conducting local as well semi-local analysis. In this study, we explore...