What does $\omega+\omega*$ denote?(model theory)

Question

In Kees Doets' Basic Model Theory, there is a lemma(3.12) as follows:

1. $$k,m\geq2^n-1\implies Sy(k,m,n).$$
2. $$m\geq2^n-1\implies Sy(\omega+\omega*,m,n).$$

where:

1. $Sy(A,B,n)$ is a notation for the situation that the Spoiler has a winning strategy in the Ehrenfeucht–Fraïssé game of n rounds, in which $A$ and $B$ are the two structures.
2. $k,m,\omega$ are order types.

What confuses me is the notation $\omega+\omega*$. $\omega$ denotes the order type of natural numbers, and $\omega*$ denotes the order type of the dual of natural numbers(the reversed order). Then what about $\omega+\omega*$? Does it denote

1. $\{0，1，2，3，…,…,ω+3,ω+2,ω+1,ω\}$, that is, $\omega$ followed by $\omega*$

or

2. $\{…,−3,−2,−1, 0，1，2，3，…\}$, that is, $\omega*$ followed by $\omega$?

Answer 1

It's the former. In general, for $A,B$ linear orders, "$A+B$" is the linear order consisting of a copy of $A$ followed by a copy of $B$.

(Incidentally, "$\zeta$" is used to denote the ordertype of the integers, so $\omega^*+\omega=\zeta$. This is your second possibility.)