Deleting new line when beginning new theorem in a list

Question

I am using the package amsthm to type my assignments and I have encountered the following problem. Here's the code I use:

\newtheorem{claim}{Claim}
:
:
\begin{enumerate} 

\item
\begin{claim}
    $lefthalf(L) := \{w_1 :  \exists w_2 \in \Sigma^*.w_1w_2 \in L.|w_1| = |w_2|\}$.
\end{claim}

\item 
{\textbf{Claim 1.}} $lefthalf(L) := \{w_1 :  \exists w_2 \in \Sigma^*.w_1w_2 \in L.|w_1| = |w_2|\}$.

\end{enumerate}

This gives the following result:

As you can see in (a), the claim begins on the second line. I would like my claim to be as in (b) where I simulate the style I want. Is there any way I could get rid of this extra newline occuring when I use newthm in a list? I have tried to change theoremstyle but couldn't get it to work.

Any ideas on how to solve this problem?

Thanks a lot.