preserve association in multivalued in solr

I have multivalued fields in my solr datasource. sample is

<doc>
<str name="id">23606</str>
<arr name="institution">
    <str>Harvard University</str>
    <str>Yale Universety</str>
    <str>Cornell University</str>
    <str>TUFTS University</str>
    <str>University of Arizona</str>
</arr>
<arr name="degree_level">
    <str>Bachelors</str>
    <str>Diploma</str>
    <str>Master</str>
    <str>Master</str>
    <str>PhD</str>
</arr>
</doc>

in the example above this user has got Bachelors degree from Harvard, Diploma from Yale, Master from Cornell, Master from TUFTS, and PhD from Arizona. now if i search for users who have Bachelors degree and graduated from Harvard, i will get this user, which is correct. MyDomain:8888/solr/mycol/select?facet=true&q=:&fq=degree_level:Bachelors&fq=institution:Harvard+University

but if i want those who have Bachelors from Cornell, i will get this user as well, which is incorrect! MyDomain:8888/solr/mycol/select?facet=true&q=:&fq=degree_level:Bachelors&fq=institution:Cornell+University
The question is: how could i preserve ordering/mapping in multivalued in solr?
Edit:
By the way, i know that i can solve my problem by creating new field to contain concatenation of the degree with university (ie, "Bachelors_Harvard University", "Diploma_Yale Universety", and so on) but i need a solution based on solr core itself as i have a lot of multivalued fields with a lot of combinations.

Below is a list of some suggestions

try using dynamic fields
<dynamicField name="degree_level_*" type="string" indexed="true" stored="true" />
and create fields dynamically while indexing degree_level_Bachelors with value Harward University and so on. so when you want to filter on Bachelors degree, filter on field degree_level_Bachelors. Similarly, if you want to allow filtering on institutions, create a dynamic field for institutions.
you can pre define how you will be storing data: <year><seperator><degree><seperator><institution><seperator><Major> etc etc.
and then filter on the reqired regex.
eg:
fq=educationDetails:2009@Bachelors@Harvard@*
this will give you all records with bachelors from Harvard in 2009. you will have to come up with the regex expressions for all the different filters.
two collections to correctly model the one-to-many relationship between user and degree queried using {!join}
one collection at a "user-degree" level of granularity that gets deduped via Solr's field collapsing support.