second order arithmetic造句
例句與造句
- Second order arithmetic is a formal theory of the natural numbers and sets of natural numbers.
- Ordinal analysis has been extended to many fragments of first and second order arithmetic and set theory.
- Recursion theory is also linked to second order arithmetic, a formal theory of natural numbers and sets of natural numbers.
- The fact that certain sets are computable or relatively computable often implies that these sets can be defined in weak subsystems of second order arithmetic.
- Many natural propositions expressible in the language of second order arithmetic are independent of Z 2 and even ZFC but are provable from projective determinacy.
- It's difficult to find second order arithmetic in a sentence. 用second order arithmetic造句挺難的
- This is equivalent to sets defined by both a universal and existential formula in the language of second order arithmetic and to some models of Hypercomputation.
- :There are extremely few " natural " mathematical statements that can be stated in second order arithmetic but are not provable in second order arithmetic.
- :There are extremely few " natural " mathematical statements that can be stated in second order arithmetic but are not provable in second order arithmetic.
- In 1858, Dedekind proposed a definition of the real numbers as Cantor in his set theory, and axiomatized in terms of second order arithmetic by Hilbert and Bernays.
- The true theory of first-order arithmetic,, is a subset of the true theory of second order arithmetic, and is definable in second-order arithmetic.
- Many mathematical theorems can be proven in much weaker systems than ZFC, such as Peano arithmetic and second order arithmetic ( as explored by the program of reverse mathematics ).
- Burgess ( 2005 ) discusses predicative and impredicative theories at some length, in the context of Frege's logic, Peano arithmetic, second order arithmetic, and axiomatic set theory.
- Slaman and W . Hugh Woodin formulated the Bi-interpretability Conjecture for the Turing degrees, which conjectures that the partial order of the Turing degrees is logically equivalent to second order arithmetic.
- For example, the set of ( codes for ) formulas of first-order Peano arithmetic that are true in " N " is definable by a formula in second order arithmetic.
- Many mathematical objects, such as fields, as well as points in effective Polish spaces, can be represented as sets of natural numbers, and modulo this representation can be studied in second order arithmetic.
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