Namespaces
Variants
Actions

Difference between revisions of "Refutable formula"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
 
Line 1: Line 1:
 +
{{TEX|done}}
 
''formally refutable formula, in a given system of formulas''
 
''formally refutable formula, in a given system of formulas''
  
Line 6: Line 7:
  
 
====Comments====
 
====Comments====
A closed formula <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080600/r0806001.png" /> in a given logical system is formally decidable (cf. [[Decidable formula|Decidable formula]]) if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r080/r080600/r0806002.png" /> is either provable or refutable.
+
A closed formula $A$ in a given logical system is formally decidable (cf. [[Decidable formula|Decidable formula]]) if $A$ is either provable or refutable.
  
 
====References====
 
====References====
 
<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
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article