Elementary function arithmetic: Difference between revisions

Revision as of 21:27, 14 July 2010

Revision as of 05:48, 15 July 2010

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In [[proof theory]], a branch of [[mathematical logic]], [[Harvey Friedman]]'s '''grand conjecture''' implies that many mathematical theorems, such as [[Fermat's last theorem]], can be proved in very weak systems.

The original statement of the conjecture from {{harvtxt|Friedman|1999}} is:

: "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, +, ''x'', exp, together with the scheme of [[mathematical induction|induction]] for all formulas in the language all of whose quantifiers are bounded."

"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,+,x,exp, together with the scheme of induction for all formulas in the

language all os whose quantifiers are bounded."

==References==