Inconsistent class
From Encyclopedia of Mathematics
A class 
of formulas in the language of a given formal theory having the property that there is a formula 
such that both 
and 
(the negation of 
) can be deduced from 
in this theory. In other words, if all formulas in 
are added to the axioms of the theory as new axioms, then in the theory obtained one can deduce both the formula 
and the formula 
.
Comments
References
| [a1] | A. Grzegorczyk, "An outline of mathematical logic" , Reidel (1974) |
| [a2] | S.C. Kleene, "Introduction to metamathematics" , North-Holland & Noordhoff (1950) pp. Chapt. XIV |
How to Cite This Entry:
Inconsistent class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Inconsistent_class&oldid=12085
Inconsistent class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Inconsistent_class&oldid=12085
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article