Are you sure you are not running Mavericks? Check under the apple menu for About this Mac.
The reason I ask is that Snow Leopard does not have Notifications, and does not use the App Store to do updates. In Snow Leopard updates are done via Software Update.
Within Snow Leopard Software Update will want to install a Mavericks migration aid. You can install this without installing Mavericks.
I am not exactly sure what the Migration Aid does, but it does not interfere with you running Snow Leopard.
Normally updates to Snow Leopard come from Software Update.
It may be that something weird is happening with the App Store thinking you have Mavericks and wanting to update it. But I don't see how it is sending you notifications if you are running Snow Leopard. If what you mean is simply that the software is there listed under the updates section, then just ignore it.
There may be vestiges of the download residing in the system. If you have the 'Find any file' app, that will seek them out and allow you to delete them. If there is but one iota of Mavericks left in your system, the system will find it and send you updates.
* Find any File, an excellent app from the App store @ £5.49 currently.
I have no connection with the developer.
I run 10.6.8 and I am getting notices about installing Mavericks too.
I have not downloaded Mavericks, lion, etc. But I HAVE download the Mac AppStore. That was listed for me as a Software Update, in the usual way - via Snow Leopard's System Software Update app.
I do not buy software from the MacAppStore; I buy directly from developers, so I had and continue to have no need for the app store. And yet... I let System Software download it.
And I answered a Question as it was installed: something like...
"How's about I send you some notices about software you don't want and can't use on your machine? It won't even look like a REAL OS notice; no - it will look like a totally FAKE and Viris-ish, Trojan-like notice on your iMac! Cool, huh? See, it looks like a notice for a phone or iPad, though your iMac is not a phonePad, yet. And get this, it does not even say what App it is from! You will never know where it came from! Cool, huh? Want some notices? Say YES!"
And I thought, sure, why not? I already let Snow Leopard's system software update send me notices, why not the Mac AppStore too?
And there ya go... a couple weeks later - yesterday! - out of the blue... a small, unannounced, and ostensibly foreign and maybe intent on harm "you are eligible to install mavericks" notice appeared! Does that sound like a something Apple would do? Send a mystery notice?
Click YES or NO. What the...? Where did this come from? And if it is some bad thing, do both buttons actually send a "yes"? Why, if it IS from Apple, does it not NOT SAY SO across the top, like other OS system notices?? No way to dismiss it except to click a button.
Reading posts today I am learning it will continue to badger me, for no good reason, and I cannot turn it off since I do not have the AppStore's preference pane in system preferences, as others using a newer OS do. If you have that pane, click it and see if you can turn off the notices.
pestering... and looking like a virus or something while doing it too. Hateful. I am looking for its pref file .plist so I can toss that and run the app and MAYbe it will ask me the question again, "Want to get some pestering notices?" and I can finally say NO!
I will delete the app but I want those prefs gone first, against the next time I install this thing.
Others have discovered these notices ARE from the Mac AppStore App, specifically being sent by an app within it called Noticeboard. https://discussions.apple.com/message/25171309#25171309
Why it sends notices to update your deleted apps I've no idea but it probably has its own list of your software (past & present) and checks for updates from that.
If you have Little Snitch you can block Noticeboard from connecting to the internet and that will stop the notices.
Very interesting and helpful info in this collection.