Elementary function arithmetic: Difference between revisions

Revision as of 13:42, 22 October 2010

Revision as of 01:11, 25 October 2010

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: "Every theorem published in the ''[[Annals of Mathematics]]'' whose statement involves only finitary mathematical objects (i.e., what logicians call an arithmetical statement) can be proved in EFA. EFA is the weak fragment of [[Peano Arithmetic]] based on the usual quantifier-free axioms for 0, 1, +, ×, exp, together with the scheme of [[mathematical induction|induction]] for all formulas in the language all of whose quantifiers are bounded."

While it is easy to construct artificial arithmetical statements that are trytrue but not provable in EFA, the point of Friedman's conjecture is that natural examples of such statements in mathematics seem to be rare. Some natural examples include consistency statements from logic, several statements related to [[Ramsey theory]] such as [[Szemeredi's lemma]] and the [[graph minor theorem]], and Tarjan's algorithm for the [[disjoint-set data structure]].

==Related systems==