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Silver's theorem shows that it cannot first fail at ℵω1 and this is provable in ZFC.
If this is provable of course it is [as bad as Ben Johnson]." Canadian sprinter Johnson was stripped of his gold medal in the 100m at the 1988 Seoul Olympics after officials discovered he was on steroids.
Like, take light, for instance: light (and this is provable!) does not just, like, stick out of a flashlight for three feet and then stop.
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This principle is provable in Peano Arithmetic.
Indeed, if \(t\) is not a proof of \(F\) then, since this statement is decidable, it can be established inside \(T\), hence in \(T\) this sentence is provable.
"In this field nothing is provable," Quinlan wrote, "but it is far from clear that they would regard less than half of 1% of their population as an unthinkable price for contemplating a conquest of western Europe".
"In this field nothing is provable, but it is far from clear that they would regard less than half of 1% of their population as an unthinkable price for contemplating a conquest of western Europe," Quinlan wrote.
It turns out that neither this hypothesis nor its negation is provable from the ZFC axioms; the question of the size of the continuum is independent of ZFC.
Since it is provable from this axiom and the previous axiom that there is a unique such set, we may introduce the notation '$\varnothing$' to denote it.
It is provable that this translation won't introduce any inconsistency into mathematics (since there are values for s), or any indeterminacy (since the embedded sentence …s…s… has the same truth value for any eligible value for s).
We also introduce a formal security model suitable for roaming service in global mobility networks and show that the proposed protocol is provable secure based on this model.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com