Your config.xml has some mistakes. Follow in this way..
< ?xml version="1.0"?>
<config>
<modules>
<my_core>
<version>0.1.0</version>
</my_core>
</modules>
<global>
<models>
<core>
<rewrite>
<store>My_Core_Model_Store</Store>
</rewrite>
</core>
</models>
</global>
</config>
and also in the model class, You need to extend the Parent Class Name. For Ex: My_Core_Model_Filename extends Mage_Core_Model_Store