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Friedman translation
・ Friedman Unit
・ Friedman's Inc.
・ Friedman's k-percent rule
・ Friedmann equations
・ Friedmann Nunataks
・ Friedmann Peak
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・ Friedmannia
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Friedman translation : ウィキペディア英語版
Friedman translation
In mathematical logic, the Friedman translation is a certain transformation of intuitionistic formulas. Among other things it can be used to show that the Π02-theorems of various first-order theories of classical mathematics are also theorems of intuitionistic mathematics. It is named after its discoverer, Harvey Friedman.
==Definition==
Let ''A'' and ''B'' be intuitionistic formulas, where no free variable of ''B'' is quantified in ''A''. The translation ''AB'' is defined by replacing each atomic subformula ''C'' of ''A'' by . For purposes of the translation, ⊥ is considered to be an atomic formula as well, hence it is replaced with (which is equivalent to ''B''). Note that ¬''A'' is defined as an abbreviation for hence

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