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

Theorem 1

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

Theorem 2

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

Title	finiteness of $C_{\cup }$ and $C_{\cap }$
Canonical name	FinitenessOfCcupAndCcap
Date of creation	2013-03-22 16:30:04
Last modified on	2013-03-22 16:30:04
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	4
Author	rspuzio (6075)
Entry type	Theorem
Classification	msc 03B22
Classification	msc 03G10
Classification	msc 03G25