hereditarily finite sets造句

例句与造句

1. The set of all well-founded hereditarily finite sets is denoted " V " ?.
2. It is V _ \ omega \ !, the class of hereditarily finite sets, with the inherited element relation.
3. The hereditarily finite sets, V ?, satisfy the axiom of regularity ( and all other axioms of ZFC except the axiom of infinity ).
4. Mainstream mathematicians consider strict finitism too confining, but acknowledge its relative consistency : the universe of hereditarily finite sets constitutes a model of Zermelo Fraenkel set theory with the axiom of infinity replaced by its negation.
5. One can interpret the theory of hereditarily finite sets within Peano arithmetic ( and certainly also vice versa ), so the incompleteness of the theory of Peano arithmetic implies that of the theory of hereditarily finite sets.
6. It's difficult to find hereditarily finite sets in a sentence. 用hereditarily finite sets造句挺难的
7. One can interpret the theory of hereditarily finite sets within Peano arithmetic ( and certainly also vice versa ), so the incompleteness of the theory of Peano arithmetic implies that of the theory of hereditarily finite sets.
8. For any finite ordinal n, the sets L n and V n are the same ( whether V equals L or not ), and thus L ? = V ? : their elements are exactly the hereditarily finite sets.
9. Instead of being considered as a subset of the natural numbers, it is also possible to encode 0 # as a subset of formulae of a language, or as a subset of the hereditarily finite sets, or as a real number.
10. We regain the two simple notions we introduced above as H ( \ omega ) being the set of hereditarily finite sets and H ( \ omega _ 1 ) being the set of hereditarily countable sets . ( \ omega _ 1 is the first uncountable ordinal .)
11. The existence of Grothendieck universes ( other than the empty set and the set V _ \ omega of all hereditarily finite sets ) is not implied by the usual ZF axioms; it is an additional, independent axiom, roughly equivalent to the existence of strongly inaccessible cardinals.
12. Notice that there are countably many hereditarily finite sets, since " V n " is finite for any finite " n " ( its cardinality is " n " & minus; 1 2, see tetration ), and the union of countably many finite sets is countable.
13. A seeming paradox, non-standard models of the theory of hereditarily finite sets contain infinite sets---but these infinite sets look finite from within the model . ( This can happen when the model lacks the sets or functions necessary to witness the infinitude of these sets . ) On account of the incompleteness theorems, no first-order predicate, nor even any recursive scheme of first-order predicates, can characterize the standard part of all such models.