The German Wikipedia page for Inflektiv also provides a synonym—Erikativ—which is "named for Erika Fuchs, who translated Mickey Mouse comics into German and used the form frequently". Going by Google's results, Erikativ (or Ericativ, sometimes with an 'e' at the end) appears to be just as popular as Inflektiv.
There is an interesting (and exhaustive) paper by a Mark Lindsay [PDF] on the subject of the Erikativ from a linguistic point of view. He states:
The German Erikativ construction (also known as the Inflektiv (Teuber 1998)) is a phenomenon that existed prior to the mid-twentieth century, but first developed widespread prominence through the German-language translations of Disney comics during the 1950’s. The translator, Erika Fuchs, used this form to describe sounds and actions of the characters (not unlike English crash! or pow!); eventually, these words evolved beyond onomatopoeic use, expanding to phrases like stare (starr) or dancing while sitting (sitzendtanz). Unlike onomatopoeias, these new forms followed a predictable pattern.
It should be noted that Teuber (1998, p. 8) describes the Inflektiv as a verb form that is non-inflected (German: nicht-flektiert); therefore, the German term Inflektiv should be translated into English as Uninflective. To avoid the confusion this causes, I shall use the alternative term, Erikativ.
Later:
Teuber (1998) argues convincingly that the Erikativ is a true verb form, as it has semantic and morphological restrictions that distinguish it from the freeform nature of interjections. Noting the common similarity between the Erikativ form and the verbal stem, he coins the term Inflektiv (‘uninflective’) to describe its lack of overt inflection.
The Erikativ is essentially the same as "actions" or "emotes" (WP) seen in most IRC channels and other chat rooms such as *dies*, *dances*, *rolls his eyes*, *coughs*, etc.
In comic lettering, emotes, when inserted within dialogue, are punctuated differently. These punctuations are called breath marks, crow's feet, cat's whiskers, or fireflies. I am unaware of any standard term that describes the "breath words" themselves.
As has been observed... Duck D. and M. Mouse; Boats Need Water to Float (New York 2009), p.87.
That would most likely be given by way of footnote in most academic papers. It is known as 'The Oxford System'. There is a Harvard System which sets out the same information slightly differently. Neither system quotes the name of the publisher, only the city and year of publication.
It is not a mistake on my part to have written 'Duck D. and M. Mouse'. With the first author quoted the forename (s) or initials follow the surname, with subsequent ones they appear in front!
Best Answer
I don't know if there's a name for such sentences themselves, but they are surely appropriate in formal English:
Bible search results for "the more". Here are only some of the various possible syntactical structures:
British National Corpus search results for "the more". Again, just a couple examples:
Wiktionary says:
The corresponding Merriam-Webster entry reads as follows:
Do note that — as the third Wiktionary example and the last two of the BNC examples quoted above demonstrate — the chain is not limited to just two items. In fact, there is no theoretical limit, only a practical one that depends entirely on context.
Also (and this is addressed by both Merriam-Webster and Wiktionary, but I think I should expressly state it here), this the is etymologically not the same as the article the. The article comes from Old English þē, a variant of sē, while the adverb comes from Old English þȳ, the instrumental case of sē and þæt. If we look at related languages, e.g. German where the article would be der, the construction "the more, the better" is still formed with a different word even today: "je mehr, je besser" (or "je mehr, desto besser"). Follow the Wiktionary link for more infos.
This construction is not limited to Germanic languages, either. Russian has "чем... тем...". French has "plus... plus...". A fellow poster provides additional information in his answer to a related question. He also simply and elegantly calls this construction the "parallel comparative", which is not a term I've used before, but one that is conveniently self-explanatory.