Determine whether these structures are is isomorphic ? ,
if they are isomorphic Show the isomorphism function and proved
if they are no isomorphic proved by an appropriate verse
A. $M_2= \langle(1,\infty),+\rangle$ , $M_1 = \langle(0,\infty),+\rangle$
attempt:
if i want to show isomphism in A. or B. i need to show .
for all sign of function $f$
1.$h(F^{M}(a_1,a_2,...a_n))=F^N(h(a_1),h(a_2),...(h(a_n))$
2.Injective function
3.Surjective function
if i try to prove isomorphic in B. between $M_2$ , $M_1$ i dont know how to prove them with in open segment
Question A
The sentence $\phi \equiv \forall x \exists y(y+y=x)$ is satisfied in $M_1$ but not $M_2$. Therefore the two structures can't be isomorphic.