Is there symbolism (or even a name) for groups of statements in which any fixed-number of them imply all the rest?
For example, in linear algebra, a basis is sometimes defined as a set of n-dimensional vectors which:
- Is linearly independent
- Spans the vector space
- Contains exactly n elements
However, it is then shown that any TWO of these statements being true implies the third is true. How would you write this symbolically? (other than $A \wedge B \Rightarrow C, A \wedge C \Rightarrow B, B \wedge C \Rightarrow A$, which does not scale well...)