Is SQL order by clause guaranteed to be stable ( by Standards)

I am using following query to query DB which have order by on two columns.

SELECT a,b,c from Table1 Order By a asc, b asc;

My question is, Is the sorting guaranteed to be stable (by Standards) or not. Though it doesn't make any sense for it to be, not be stable, But i ask this because I read on net that

The standard does not prevent the use of a stable sort, but it also does not require it.