I've always considered a cadence to be the last two harmonies or chords in a phrase or line of music. Reading about the Andalusian cadence, it looks like it needs all four chords to qualify. I prefer to call it the Spanish sequence, so why 'cadence'?
Cadere means to fall.
So if something falls even more than I - IV - V -I it is the spanish Sequence or better the Andalusian cadence as it falls step by step: i - VII - VI - V
a cadence to be the last two harmonies or chords in a phrase or line of music
A harmonic cadence is a progression of (at least) two chords that concludes a phrase, section, or piece of music. A rhythmic cadence is a characteristic rhythmic pattern that indicates the end of a phrase. A cadence is labeled more or less "weak" or "strong" depending on its sense of finality.
What constitutes a Cadence?
The following translation of German wikipedia says that the cadence is the chord progression to complete a piece (ending), and the term became ambiguous as it was adapted to design other usual harmony patterns
In today's music theory cadence (Italian cadenza, from Latin cadere, 'fall') usually designates a chord progression that articulates the completion of a section or a whole piece.
Since the 18th century, the term is ambiguous. Because since then it is also used in the harmony theory for certain chord progressions, which are explained to the basic building block of harmony and do not necessarily represent a conclusion.
Great influence here was the music-theoretical writings of Jean-Philippe Rameau. In the later 19th century Hugo Riemann also declared "cadence" to be the principle of musical form as a whole. Against this background, terms such as "extended cadence" and "full cadence" have become established.
In an even more general sense, the term is sometimes used today for certain clichéd harmonic sequences, without them becoming a theoretical principle (eg Andalusian cadence).
Personally, I take the view Caplan gives in The Classical Cadence: concepts and misconceptions. Especially his comments about the 'plagal' cadence.
But about the Andalusian cadence, I think the typical thing it to repeat it like a ground bass...
||: i VII VI V :||
...that brings up the question: if it keeps repeating - and therefore nothing stops - does the chord progression necessarily create a cadence?
You could ask a similar question with a different ground bass: Pachelbel's Canon. Does each variation coincide with a cadence?
I suppose "yes." Each repetition is a new phrase with an ending. The rhythm doesn't stop so I guess we can say the phrases and cadences are elided.
So let's continue with "yes" we get cadences at the repeats. The actual cadence is then...
...V :||: i...
It's just a variety of authentic cadence.
Regarding all four chords, I consider the idea to be a chord progression not a cadence. If someone calls it Andalusian cadence, I take the meaning to be about a chord progression and not the formal (structural) meaning of cadence.
On the other hand, if someone is talking about sonata form, tonicization, modulation, etc. I expect them to know the formal meaning and use the term properly.