Sentence examples for arithmetic theory from inspiring English sources

Artin's early work centred on the analytical and arithmetic theory of quadratic number fields.

IA [25] is a range arithmetic theory which is firstly presented by Moore in 1962.

In general, for consistent theories T, T ′ containing a sufficiently strong fragment of arithmetic, theory T ′ is of higher consistency strength than theory T just in case T ′ proves that T is consistent.

In particular, Feferman pointed to intensional problems connected to the notion of axiomhood by exhibiting a non-standard though extensionally (i.e., numerically) correct binumeration of the arithmetic theory T under consideration, for which the (intensionally incorrect) consistency statement can be proved by T.

Briefly, Noether subsumed the structure theory of associative algebras and the representation theory of groups into a single arithmetic theory of modules and ideals in rings satisfying ascending chain conditions.

More recently, Curtis Franks takes up the issue of the second incompleteness theorem for weak arithmetic theories in his 2009, challenging Pudláak's argument that an intensionally adequate proof predicate can be given for Q.

Like the axioms for geometry devised by Greek mathematician Euclid (c. 300 bce), the Peano axioms were meant to provide a rigorous foundation for the natural numbers (0, 1, 2, 3,…) used in arithmetic, number theory, and set theory.

Although Principia succeeded in providing detailed derivations of many major theorems in finite and transfinite arithmetic, set theory, and elementary measure theory, two axioms in particular were arguably non-logical in character: the axiom of infinity and the axiom of reducibility.

Books VII IX deal with what the Greeks called "arithmetic," the theory of whole numbers.

Right now, the Generator covers six subjects: arithmetic, number theory, algebra, calculus, linear algebra and statistics.

Social competence subscale scores were positively correlated with arithmetic and theory of mind scores.