recursive ordinal造句
例句与造句
- It is trivial to check that \ omega is recursive, the countably many recursive ordinals.
- The primitive recursive ordinal functions are the same as the primitive recursive set functions that map ordinals to ordinals.
- Recursive ordinals ( or computable ordinals ) are certain countable ordinals : loosely speaking those represented by a computable function.
- Kleene ( 1938 ) described a system of notation for all recursive ordinals ( those less than the Church Kleene ordinal ).
- This relationship between lightface sets and their indices is used to extend the lightface Borel hierarchy into the transfinite, via recursive ordinals.
- It's difficult to find recursive ordinal in a sentence. 用recursive ordinal造句挺难的
- The operations of addition, multiplication and exponentiation are all examples of primitive recursive ordinal functions, and more general primitive recursive ordinal functions can be used to describe larger ordinals.
- The operations of addition, multiplication and exponentiation are all examples of primitive recursive ordinal functions, and more general primitive recursive ordinal functions can be used to describe larger ordinals.
- Any ordinal smaller than a recursive ordinal is itself recursive, so the set of all recursive ordinals forms a certain ( countable ) ordinal, the Church-Kleene ordinal ( see below ).
- Any ordinal smaller than a recursive ordinal is itself recursive, so the set of all recursive ordinals forms a certain ( countable ) ordinal, the Church-Kleene ordinal ( see below ).
- It is tempting to forget about ordinal notations, and only speak of the recursive ordinals themselves : and some statements are made about recursive ordinals which, in fact, concern the notations for these ordinals.
- It is tempting to forget about ordinal notations, and only speak of the recursive ordinals themselves : and some statements are made about recursive ordinals which, in fact, concern the notations for these ordinals.
- Thus, \ omega _ 1 ^ { \ mathrm { CK } } is the smallest non-recursive ordinal, and there is no hope of precisely describing any ordinals from this point on & mdash; we can only " define " them.
- A fully specified extension beyond the recursive ordinals is thought to be unlikely; e . g ., Pr?mel " et al . " [ 1991 ] ( p . 348 ) note that in such an attempt " there would even arise problems in ordinal notation ".
- The existence of any recursive ordinal that the theory fails to prove is well ordered follows from the \ Sigma ^ 1 _ 1 bounding theorem, as the set of natural numbers that an effective theory proves to be ordinal notations is a \ Sigma ^ 0 _ 1 set ( see Hyperarithmetical theory ).
- The set of recursive ordinals is an ordinal that is the smallest ordinal that " cannot " be described in a recursive way . ( It is not the order type of any recursive well-ordering of the integers . ) That ordinal is a countable ordinal called the Church Kleene ordinal, \ omega _ 1 ^ { \ mathrm { CK } }.
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