The phrase "arithmetical structure" is correct and usable in written English.
It can be used in contexts related to mathematics, computer science, or any field that involves numerical systems and their properties.
Example: "The study of arithmetical structure is essential for understanding the foundations of number theory."
Alternatives: "numerical framework" or "mathematical structure".
Further, the arithmetical structures that invalidate such arguments pose deep problems for inferences from statistical regularities to conclusions about causal relations.
Section 1 provides a brief history of Simpson's Paradox, a statement and diagnosis of the arithmetical structures that give rise to it, and the boundary conditions for its occurrence.
However, once the arithmetical structures that underlie arguments like the one above are made explicit, the structures provide a rich resource for providing causal models for actual and possible causal systems that are initially puzzling and can appear to be impossible.
Namely, it is possible to conclude that any theory F satisfying the conditions of the theorem must possess, in addition to the intended interpretation or "standard model" (in the case of arithmetical theories, the structure of natural numbers), non-intended interpretations or "non-standard models"—that no such theory can rule out the latter and fix uniquely the intended interpretation.
Of course solving arithmetical problems in arithmetic is in some cases practically impossible.
Let N be a normal subgroup of a group G. Clearly N is the union of some conjugacy classes of G. So, it is interesting to decide the structure of N by some arithmetical properties of the G-conjugacy class contained in N, for example, [3, 6, 7].
The EST-SSR frequency is dependent on several factors such as genome structure or composition [ 58], arithmetical method for SSR detection, and the parameters for exploration of microsatellites.
The following example is a typical arithmetical problem that is expressed by the triplet structure model in a combination story: {There are 3 white rabbits (first existence sentence).
The following is a typical arithmetical problem that is expressed by the triplet structure model in a decrease story: {There are 5 apples (first existence sentence).
His 1959 paper "Computing Degrees of Unsolvability" obtained semantical completeness results for higher levels of arithmetical complexity, and underlies current methodology in studies of computable structures.
