Basically from the Sygate support forum ...(Which is now Owned by Symantec
SVCHOST.EXE is a Generic Service Host Process for Win32 Services. It does require Internet access for such things as Windows Update, but it does not need to "act as server." The recommendation is to set to Allow or to Ask. You will normally see several instances of svchost as active processes.
ntoskrnl.exe Process Name: Microsoft Boot Up ... ntoskrnl.exe is a critical process in the boot-up cycle of your computer. It should not require internet access. (Personal note ... I have this one set to Ask)
You might receive pop up messages in the lower right corner of the screen concerning either of these being blocked. Checking the box to disable this pop up might not work ... and it keeps happening.
This is a known bug and I understand Sygate is addressing it. These notification messages can be disabled under Tools >> Options >> Hide Notification Messages.
Sygate® Personal Firewall
Sygate® Personal Firewall Pro
To fix this issue.
Open up the Sygate console menu.
Click Tools -> Options
In the [General] Tab place a check in the Hide notification messages block.
Click OK and close the console.
No more notification messages will appear. The Icon will flash red on Severe Alerts. Click the Icon for more information on the alert.
ntoskrnl.exe - NT Kernel & System is a standard Windows service that initializes the kernel and drivers needed during a session.
I'm going say it's a typo but I'm not home to check. The reason I say it's a typo is when the Sygate Pop Up Notified my I did a google search and received numerous hits. I just googled ntkernsol.exe didn't receive any.
Ep, glad to see you come back and tidy up...did want to ask a one day favor, I want to enhance my resume , was hoping you could make me administrator for a day, if so, take me right off since I won't be here to do anything, and don't know the slightest about the board, but it would be nice putting "served administrator osnn", if can do, THANKS