Sentence examples for postulates with from inspiring English sources

Let A2 be the theory generated by the Peano postulates with choice (in the general semantics).

Accordingly, by a model of analysis we will mean a general model of the Peano postulates with choice.

By the ω-rule we mean the infinitary rule of inference that infers ∀x φ(x) from the premisses φ(0), φ(1), φ(2), ….   Suppose we add this rule to the usual logical apparatus, and see what is then deducible from the Peano postulates with choice.

The operation of contraction (referring to the removal of knowledge from a knowledge base) has been extensively studied in the research field of belief change, and different postulates (e.g., the AGM postulates with recovery, or relevance) have been proposed, as well as several constructions (e.g., partial meet) that allow the definition of contraction operators satisfying said postulates.

Euclid saw farther, for coherent geometries (known as non-Euclidean geometries) can be produced by replacing the fifth postulate with other postulates that contradict Euclid's choice.

As has been postulated, with much hand-wringing, it was obvious to many that the leave campaign didn't believe it would win, merely wishing to register a protest, and was thus left thinking: what have we done?

The early 19th-century revival of pure geometry produced the discovery that Euclid had devoted his efforts to only one of several comprehensive geometries, the others of which can be created by replacing Euclid's fifth postulate with another about parallels.

The variability of those genes had been postulated with the progression of the disease.

Various mechanisms have been proposed and different chemicals have been postulated with no confirmation.

First, for each outcome variable a saturated model will be postulated, with the primary or secondary outcomes as dependent variables.

A role for ATP in bladder dysfunction has been postulated with increased ATP release associated with sensory disorders such as interstitial cystitis [ 9] and painful bladder syndrome [ 10].