Difference between revisions of "Refutable formula"
From Encyclopedia of Mathematics
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''formally refutable formula, in a given system of formulas'' | ''formally refutable formula, in a given system of formulas'' | ||
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| − | A closed formula | + | A closed formula $A$ in a given logical system is formally decidable (cf. [[Decidable formula|Decidable formula]]) if $A$ is either provable or refutable. |
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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> S.C. Kleene, "Introduction to metamathematics" , North-Holland (1959) pp. 194ff</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> S.C. Kleene, "Introduction to metamathematics" , North-Holland (1959) pp. 194ff</TD></TR></table> | ||
Latest revision as of 17:30, 30 April 2014
formally refutable formula, in a given system of formulas
A closed formula of the given system whose negation can be deduced in this system.
Comments
A closed formula $A$ in a given logical system is formally decidable (cf. Decidable formula) if $A$ is either provable or refutable.
References
| [a1] | S.C. Kleene, "Introduction to metamathematics" , North-Holland (1959) pp. 194ff |
How to Cite This Entry:
Refutable formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Refutable_formula&oldid=32002
Refutable formula. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Refutable_formula&oldid=32002
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article