reverse mathematics造句

• Most reverse mathematics research focuses on subsystems of second-order arithmetic.
• This subsystem has an important role in reverse mathematics.
• Reverse mathematics also clarifies the extent and manner in which classical mathematics is nonconstructive.
• The ineffectiveness of the completeness theorem can be measured along the lines of reverse mathematics.
• Simpson ( 1999 ) discusses many aspects of second-order arithmetic and reverse mathematics.
• See reverse mathematics for other relations between determinacy and subsystems of second-order arithmetic.
• In particular, the real numbers are also studied in reverse mathematics and in constructive mathematics.
• The subsystem RCA 0 is the one most commonly used as a base system for reverse mathematics.
• For example, in reverse mathematics, people often work with systems much weaker than Peano arithmetic.
• The program of reverse mathematics uses these subsystems to measure the noncomputability inherent in well known mathematical theorems.
• One striking phenomenon in reverse mathematics is the robustness of the " Big Five " axiom systems.
• In 2009 he was the G鰀el Lecturer ( " Reverse mathematics : the playground of logic " ).
• However these researches are not philosophies of mathematics but rather the study of restricted forms of reasoning similar to Reverse Mathematics.
• Other areas which he has contributed to include bounded arithmetic, bounded reverse mathematics, and lower bounds in propositional proof systems.
• In fact, they prove that under a weak set of assumptions, the two are equivalent, an example of reverse mathematics.
• The axiom systems most often considered in reverse mathematics are defined using axiom schemes called "'comprehension schemes " '.
• The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory.
• In some cases these questions may be sufficiently answered through the study of formal theories, in disciplines such as reverse mathematics and computational complexity theory.
• The body of research in reverse mathematics has established that weak subsystems of second-order arithmetic suffice to formalize almost all undergraduate-level mathematics.
• The reason that reverse mathematics is not carried out using set theory as a base system is that the language of set theory is too expressive.