NSA can be introduced in multiple ways. Instead of choosing one option, these notes include three introductions. Section 1 is best-suited for those who are familiar with logic, or who want to get a flavor of model theory. Section 2 focuses on some common ingredients of various axiomatic approaches to NSA, including the star-map and the Transfer principle. Section 3 explains the ultrapower const...

The thesis of this book is that Löwenheim’s and Skolem’s work on what is now known as the downward Löwenheim–Skolem theorem developed directly from Schröder’s Algebra der Logik, which was itself an avowed elaboration of the work of the American logician Charles S. Peirce and his student O. H. Mitchell. We have been unable to detect any direct influence of Frege, Russell, or Hilbert on the devel...

Many source localization methods neglect the anisotropic conductivity of brain tissues, although it has a big influence on the localization problem. In this study, we evaluated the dipole localization error due to neglecting the anisotropic properties of the conductivity in a realistic head model (built from T1 and diffusion tensor MRI) calculated using a FDM method. Results show that the mean ...

Using the Skolem-Mahler-Lech theorem, we prove a dynamical Mordell-Lang conjecture for semiabelian varieties.

a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

The disjunctive skolem chase is a sound, complete, and potentially non-terminating procedure for solving boolean conjunctive query entailment over knowledge bases of existential rules. We develop novel acyclicity cyclicity notions this procedure; that is, we sufficient conditions to determine termination non-termination. Our empirical evaluation shows our are significantly more general than exi...