Words near each other
 ・ Craig Yeast ・ Craig Yoe ・ Craig Young ・ Craig Young (cricketer) ・ Craig Young (disambiguation) ・ Craig yr Aderyn ・ Craig yr Allt ・ Craig Zadan ・ Craig Zetter ・ Craig Ziadie ・ Craig Zimmerman ・ Craig Zisk ・ Craig Zobel ・ Craig Zucker ・ Craig's Brother ・ Craig's theorem ・ Craig's Wife ・ Craig's Wife (film) ・ Craig, Alaska ・ Craig, California ・ Craig, Colorado ・ Craig, Indiana ・ Craig, Iowa ・ Craig, Missouri ・ Craig, Modoc County, California ・ Craig, Montana ・ Craig, Nebraska ・ Craig-Beasley House ・ Craig-Bryan House ・ Craig-Cefn-Parc television relay station
 Dictionary Lists
 mini英和辞書
 mini和英辞書
 Webster 1913
 Latin-English
 FOLDOC
 Wikipedia English
 ウィキペディア
 翻訳と辞書　辞書検索 [ 開発暫定版 ]
 スポンサード リンク
 Craig's theorem ： ウィキペディア英語版
Craig's theorem
In mathematical logic, Craig's theorem states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same mathematician, William Craig.
== Recursive axiomatization ==

Let $A_1,A_2,\dots$ be an enumeration of the axioms of a recursively enumerable set T of first-order formulas. Construct another set T
* consisting of
:$\underbrace_i$
for each positive integer ''i''. The deductive closures of T
* and T are thus equivalent; the proof will show that T
* is a decidable set. A decision procedure for T
* lends itself according to the following informal reasoning. Each member of T
* is either $A_1$ or of the form
:$\underbrace_j.$
Since each formula has finite length, it is checkable whether or not it is $A_1$ or of the said form. If it is of the said form and consists of ''j'' conjuncts, it is in T
* if it is the expression $A_j$; otherwise it is not in T
*. Again, it is checkable whether it is in fact $A_n$ by going through the enumeration of the axioms of T and then checking symbol-for-symbol whether the expressions are identical.

ウィキペディアで「Craig's theorem」の詳細全文を読む

スポンサード リンク
 翻訳と辞書 : 翻訳のためのインターネットリソース