A class $K$ of formulas in the language of a given formal theory having the property that there is a formula $\phi$ such that both $\phi$ and $\neg\phi$ (the negation of $\phi$) can be deduced from $K$ in this theory. In other words, if all formulas in $K$ are added to the axioms of the theory as new axioms, then in the theory obtained one can deduce both the formula $\phi$ and the formula $\neg\phi$.


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
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article