Sentence examples for arithmetical theory from inspiring English sources

Hermite was a major figure in the development of the theory of algebraic forms, the arithmetical theory of quadratic forms, and the theories of elliptic and Abelian functions.

The second argument is that psychologism seems incompatible with standard arithmetical theory, which insists that infinitely many numbers actually exist, because clearly there are only a finite number of ideas in human heads.

Robert K. Meyer (1976) seems to have been the first to think of an inconsistent arithmetical theory.

Direct reference to polynomial rates of growth is also avoided in the formulation of the first-order arithmetical theory now known as \ \text{I}\Delta_0\) (which was originally introduced by Parikh (1971) under the name \ \textsf{PB}\)).

One extension is to add a binary modality ⊳, where for a given arithmetical theory T, the modal sentence A ⊳ B is meant to stand for "T+B is interpretable in T+A".

4.5 Bounded arithmetic Another connection between logic and computational complexity is provided by first-order arithmetical theories which are similar in form to familiar systems such as Primitive Recursive Arithmetic and Peano arithmetic.

The papyri show the astrologers of Greek Egypt happily using Greek versions of Babylonian arithmetical theories for computing planet positions.

The Babylonians had no geometrical models but instead focused on devising arithmetical theories that had real predictive power.

By about 300 bce the temple scribes achieved a far more sophisticated method of predicting planetary behaviour on the basis of complex arithmetical theories.

Thus, sufficiently strong consistent arithmetical theories cannot prove their own consistency.

But these weak background theories only allow very weak arithmetical theories to be derived from Basic Law V (Burgess 2005).