Largest number?

whats the largest number you can express without involving infinities?

v(y)=TREE(TREE(...(...(10)))), with y TREE() functions's ;see http://en.wikipedia.org/wiki/Kruskal's_theorem
k(x,y)=v(v(v(...(x)))) , with y v() functions
b(x,y)=b(b(b(...(x)))) with y b functions, each is abstraction step of v() to k(), counting the abstraction level
c(x,y)=c(c(c(c(...(x))))) with y c functions, each is abstraction step of k() to b(), counting the abstraction level
z(x,y)=z(z(z(z(...(x))))) with y z functions each is abstraction step of c() to b(), counting the abstraction level
Number is z(z(10,10),z(10,10))