How to grep string from log files on multiple servers into one single file on server1?

Hello guys,

A bit of help on a matter in which I was not able to find any kind of hints anywhere and I would like to know if you guys have an idea:

So, I am having the following 32 servers:
server1
server2
server3
.
.
server32

The list is stored in a file named hosts.

In each of this servers, I have 8 logfiles similar to the following:
/path/to/file/logfile.log
/path/to/file/logfile.1.log
/path/to/file/logfile.2.log
/path/to/file/logfile.3.log

Now, the dirty part:
I need to pull out all of the errors and warnings lines from these 8 files into one single txt file.

I was able to build up the following command:
Code:for host in `cat hosts; do ssh -qo StrictHostKeyChecking=no $host "hostname; cd /path/to/file/; echo $host; grep -i 'error' *.log > error.txt";doneBut this stores a file named error.txt on each server, in that specific path. And that is the part I am not a fan of.

Now, I would like to run this command only on server1 and the outputs from greping the log files from each server to be stored in one single file in server1. I am not too happy in using scp transfers from each server and then cat all the files into one single file on server1.
So, is there a way I can change the code above so that, when I run the command on server1, it builds one single file on server1 with all the grep results from each server?

Thanks in advance!