Thus, the assertion $A|B$ means that $A$ and $B$ are incompatible, i.e. are not true simultaneously. All other logical operations can be expressed by the Sheffer stroke. For example, the assertion $\neg A$ (the negation of $A$) is equivalent to the assertion $A|A$; the disjunction $A\lor B$ of two assertions $A$ and $B$ is expressed as:
|||H.M. Sheffer, "A set of five independent postulates for Boolean algebras, with applications to logical constants" Trans. Amer. Math. Soc. , 14 (1913) pp. 481–488|
The Sheffer stroke operation is also called alternative denial.
|[a1]||S.C. Kleene, "Introduction to metamathematics" , North-Holland (1950) pp. 139|
|[a2]||W. Marek, J. Onyszkiewicz, "Elements of logic and the foundations of mathematics in problems" , Reidel & PWN (1982) pp. 4|
Sheffer stroke. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Sheffer_stroke&oldid=35098