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As I understand from the Wikipedia article, "set comprehension" is an expression like

{ x | x ∈ R, 0<x<1}

which is familiar to everyone who reads mathematical literature, but I have never seen an equvalent for naming such expressions in the Russian literature. On this forum 3 variants are proposed: "ZF-выражение" and two analogs of "list comprehension", which is "Конструктор списка" or "списковое включение", .

The first and second variants look too programming-related. The third variant looks more "mathematical", but it seems to be uncommon among mathematicians.

Is there a better translation? Should the translation differ between programming and mathematical contexts?

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  • As a mathematician (Russian is not my native language), I would find ZF-выражение to be strange, although I know where it comes from. Why not something like множественное обозначение? – KCd Dec 10 '12 at 19:45
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    @KCd I am not a mathematician (Russian is my native language) I would readily confuse "множественное обозначение" for an antonym of "единственное обозначение". – Sergey Kalinichenko Dec 10 '12 at 19:50
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    @dasblinkenlight: Oops! Let me try that again. How about теоретико-множественное обозначение? – KCd Dec 10 '12 at 19:54
  • @KCd I'm agree with dasblinkenlight. Another argument against множественное обозначение is that множественное обозначение should be translated as "multiple designation", but not "set designation". – Sergey Dec 10 '12 at 19:54
  • @Sergey: what about my second suggestion? – KCd Dec 10 '12 at 19:55
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I will throw my two cents in. :-)

As I remember from school and university the vertical line "|" in the notation {x|...} was read as "такой что". It was kind of the term for the symbol: symbol "такой что". We did not have the term for the whole expression but the vertical line is the most important symbol there. So, the logical name for the whole expression would be "определение множества через знак "такой что"" - which sounds a bit ugly.

Nevertheless, I searched in Russian wikipedia for mathematical symbols and found this page. If you search on the page for the "{ | }", you will find in the 3rd column the name and the pronunciation of the expression. The name is: "Множество элементов, удовлетворяющих условию". So, the answer to the OP will be "выражение для множества элементов удовлетворяющих условию".

I know it is not short, but it seems to be the official name for the mathematical context. Now we see why it is sometimes necessary to borrow terms from other languages. :-)

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  • Maybe not выражение, but описание множества элементов, удовлетворяющих условию. It's a bit shorter. – Sergey Dec 12 '12 at 18:27
  • @Sergey: An idea brought by shabunc's answer, if we can invent terminology, how about: запись/описание множества через предикат or предикативная запись множества. – farfareast Dec 12 '12 at 18:57
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As for programming, set comprehensions, by analogy with list comprehensions (which are usually called генераторы списков), are called генераторы множеств.

As for maths, in Russian tradition, as far as I know, such constructions ({x | where x have following properties} are called just sets (множества), but when we want to emphasise the fact that there are some properties defining the set, we call such properties характеристические свойства множества. So, my 2 cents are - множество с заданными характеристическими свойствами or множество, определяемое через характеристические свойства.

The word предикат is also used instead of характеристическое свойство. Also, I've seen phrase множество, заданное порождающей процедурой.

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  • Характеристические свойства is a good term. As far as I (vaguely) remember from school and see in wikipedia the second part of the notation {x|x ∈ R, 0<x<1}, i.e. after the vertical line is called характеристическое свойство. So, in a way as I suggested that the vertical line is the most important in the notation, @shabunc is suggesting that we can name notation after the second part. – farfareast Dec 11 '12 at 16:00
  • Procedural clarification, mostly at @KCd: are we looking for the name of notation, or for the collective name of what this notation expresses. In the first case we will need to say выражение определяющее множество через характеристическое свойство, in the second case множество, определяемое через характеристические свойства ((c) shabunc). In English ("set comprehension") seems to be a bit vague: is it a name for expression or for the results of such expressions. In Russian there is no short name that would have the same vagueness. – farfareast Dec 11 '12 at 17:07
  • @farfareast - выражение определяющее множество через характеристическое свойство is a good phrase, but as to me, it can me mixed with shabunc's last variant, so it will become выражение определяющее множество через порождающую процедуру. – Sergey Dec 12 '12 at 18:23
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    @Sergey: To me порождающая процедура sounds to programmer-ish. Didn't you asked for mathematical domain acceptable term? – farfareast Dec 12 '12 at 19:00
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The ZF axiom schema of (restricted) comprehension is called Схема выделения. Set comprehension itself is sometimes called выделение (из множества), though this is rare.

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