This is a **list of order types**, sorted by the set inclusion relation and by cardinality.

## Finite Edit

These ordinals have a cardinality of less than aleph null.

## Countably Infinite Edit

These ordinals have a cardinality equal to aleph null.

- Order type omega
- Order type omega plus one
- Order type omega plus two
- Order type omega times two
- Order type omega times two plus one
- Order type omega times three
- Order type omega squared
- Order type omega squared plus one
- Order type omega squared times two
- Order type omega cubed
- Order type omega cubed plus omega
- Order type omega to the fourth
- Order type omega to the omega
- Order type epsilon naught

### Non-Ordinal, Aleph Null Edit

- Order type omega star
- Order type omega star plus omega
- Order type eta
- Order type one plus eta
- Order type eta plus one
- Order type one plus eta plus one
- alpha order types where p has a cardinality greater than zero and less than .

## Uncountable Edit

These ordinals have a cardinality greater than or equal to aleph one.

### Non-Ordinal, Aleph OneEdit

- Order type lambda
- Order type one plus lambda
- Order type lambda plus one
- Order type one plus lambda plus one
- Alpha order types where p has a cardinality of .
- Alpha-plus order types where p has a cardinality greater than one and less than

### Non-Ordinal, Greater Than Aleph OneEdit

- and where p has a cardinality greater than