## Lists, Ordered sets, Multisets and sets (LOMS)

One way to strengthen the foundations of mathematics is to think more carefully about how we organize our basic objects, which end up intimately connected with the four most common data structures: Lists, Ordered sets, Multisets and Sets (LOMS for short) . In our MathFoundations series we have introduced a new framework for both the use and notation for these structures.

We want that the form of a mathematical object reflects its function.

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We want that the form of a mathematical object reflects its function.

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**list**is an ordered collection of mathematical objects in which repetitions are allowed. A list is expressed with square brackets [ ...] and with objects separated by commas.An

**ordered set**, or**oset**, is an ordered collection of distinct mathematical objects, so that repetitions are not allowed. An oset is expressed with braces { ...} and with objects separated by commas.A

**multiset,**or**mset,**is an unordered collection of mathematical objects in which repetitions are allowed. An mset is expressed with square brackets [ ...] and with objects separated by spaces.An

**set**is an unordered collection of distinct mathematical objects, so that repetitions are not allowed. A set is expressed with braces { ...} and with objects separated by spaces.