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You have a list of expressions, some of which are a single word and some of which multi-word expressions. How do you call such a collection? actually mathematically speaking I mean the case of a set, not a list with possibly repeating expressions.

Would you call it a dictionary? I assume not. A lexicon?

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  • Thanks for commenting. As written, each expression is one or more words – Matan Jul 19 '16 at 6:01
  • @jlawler while you were busy trolling the question, someone actually answered. Constructively speaking, I think we can both delete our silly comments trail here now, and/or fix up the question with an edit if necessary ― in order to clean up this page. – Matan Jul 21 '16 at 5:44
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The basic unit of meaning in a language, whether a single word or a multi-word expression with some fixed meaning, is lexeme. A language's stock of lexemes is, indeed, its lexicon.

Per the Wikipedia article on lexemes:

A lexeme is a unit of lexical meaning that exists regardless of the number of inflectional endings it may have or the number of words it may contain.

And

A lexicon consists of lexemes.

And following that link to the corresponding article on lexicons, we learn that not only does a lexicon "consist of" lexemes but stronger:

In linguistics, a lexicon is a language's inventory of lexemes.

Though whether a lexicon necessarily includes set phrases appears to vary with the specific linguistic discipline:

Linguistic theories generally regard human languages as consisting of two parts: a lexicon, essentially a catalogue of a language's words (its wordstock); and a grammar, a system of rules which allow for the combination of those words into meaningful sentences. The lexicon is also thought to include bound morphemes, which cannot stand alone as words (such as most affixes).
In some analyses, compound words and certain classes of idiomatic expressions and other collocations are also considered to be part of the lexicon.

Finally, in re the relationship between dictionaries (concrete representations) and lexicons (abstract inventory):

Dictionaries represent attempts at listing, in alphabetical order, the lexicon of a given language; usually, however, bound morphemes are not included.

So, short story, the word you're looking for, the complete set of unique (non-repeating) lexemes (words or multi-word expressions) of a language (or any other collection) is lexicon (or sometimes wordstock).

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