Does prior conviction and incarceration constitute an element of the crime charged?

In addition, many cases stand for the proposition that the prior conviction and incarceration provision of former section 667 does not constitute [53 Cal.3d 474] an "element" of that "offense." Over 80 years ago, for example, in People v. Oppenheimer, supra, 156 Cal. 733, 106 P. 74, we addressed a claim that a defendant, charged with assault with a deadly weapon by a person serving a life sentence, had a right to "admit" he was serving a life sentence and preclude the jury from learning of that fact. We rejected the claim, noting that the life sentence status was "essential" to the "public offense" that was charged, and that contrary to the defendant's view, sections 1025 and 1093 "have reference exclusively to those cases where a previous conviction of some other and distinct offense is alleged for the purpose of enabling the court to impose a greater punishment than is authorized for the offense charged when there is no prior conviction (see Pen.Code, secs. 666, 667 ...) and can have no application where the fact of the prior conviction is an essential element of the offense charged." (Id., at p. 738, 106 P. 74, italics added.)