We employ an infinite-signature Hrushovski amalgamation construction to yield two results in Recursive Model Theory. The first result, that there exists a strongly minimal theory whose only recursively presentable models are the prime and saturated models, adds a new spectrum to the list of known possible spectra. The second result, that there exists a strongly minimal theory in a finite langua...

A: a locally presentable category.

Are all subcategories of locally finitely presentable categories that are closed under limits and λ-filtered colimits also locally presentable? For full subcategories the answer is affirmative. Makkai and Pitts proved that in the case λ = א0 the answer is affirmative also for all iso-full subcategories, i. e., those containing with every pair of objects all isomorphisms between them. We discuss...

We study integrable and superintegrable systems with magnetic field possessing quadratic integrals of motion on the three-dimensional Euclidean space. In contrast case without vector potential, corresponding may no longer be connected to separation variables in Hamilton-Jacobi equation can have more general leading order terms. focus two cases extending physically relevant cylindrical- spherica...