Sentence examples for an arithmetical from inspiring English sources

The first incompleteness theorem tells us that in any consistent formal theory whose theorems are recursively enumerable and which entails a certain (rather limited) amount of arithmetic, there will be an arithmetical sentence such that neither it nor its negation is provable.

Rules of inference also get expressed in the arithmetized form: For example, there is an arithmetical formula M x, y, z) which is true exactly when one has an application of a standard rule of inference "Modus Ponens" at hand; i.e., for some formulas A and B, x = ⌈A⌉, y = ⌈A → B⌉ and z = ⌈B⌉.

For example, it is easy to make a possible worlds model to show that GL does not prove □p ∨ □¬p, so by Solovay's theorem, there is an arithmetical sentence f(p) such that Peano Arithmetic does not prove Prov(⌈f(p)⌉) ∨ Prov(⌈¬f(p)⌉).

"It's an arithmetical fact".

It's a cumulative process but never merely an arithmetical one.

This all means that 2015 will be a year in which politics takes an arithmetical turn.

n: number of samples a: arithmetical media of Ab titre (Reed and Muench) *: Significantly different (p < 0.05) Our results suggest the virus is circulating with a high prevalence on the analysed equine population, in accordance with other sero-prevalence data [ 17, 18], and confirm previous reports [ 19] about the acquisition of EHV-2 at earlier ages.

The main contribution of this research is a mathematical model to build an exact arithmetical unit able to represent without error rational numbers in positional notation system.

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".

Livingstone majors on "police numbers," continuing an interminable arithmetical tiff with Johnson, whose main soundbite is, admittedly, as dodgy as his one on council tax.

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