On subshifts with slow forbidden word growth

In this work, we treat subshifts, defined in terms of an alphabet $A$ and (usually infinite) forbidden list $F$, where the number $n$-letter words $F$ has "slow growth rate" $n$. We show that such subshifts are well-behaved several ways; for instance, they boundedly supermultiplicative as by Baker Ghenciu have unique measures maximal entropy with K-property which satisfy Gibbs bounds on large (measure-theoretically) sets. The main tool our proofs is a more general result states bounded supermultiplicativity sort measure-theoretic specification property together imply uniqueness MME bounds. also some well-known classes can be treated results, including symbolic codings f(x) = $\alpha + \beta x$ (the so-called $\alpha$-$\beta$ shifts) density Stanley.