# finiteness of $C_{\cup}$ and $C_{\cap}$

###### Theorem 1

For any set $L$ and any subsets $X$ and $Y$ of $L$, the consequence operator $C_{\cap}(X,Y)$ is finitary.

###### Theorem 2

For any set $L$, any subsets $X$ of $L$, and any finite subset $Y$ of $L$, the consequence operator $C_{\cap}(X,Y)$ is finitary.

Title finiteness of $C_{\cup}$ and $C_{\cap}$ FinitenessOfCcupAndCcap 2013-03-22 16:30:04 2013-03-22 16:30:04 rspuzio (6075) rspuzio (6075) 4 rspuzio (6075) Theorem msc 03B22 msc 03G10 msc 03G25