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=31460
Inconsistent class. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Inconsistent_class&oldid=31460
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article