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{\bf Ralph Howard, Gyula K\'arolyi and L\'aszl\'o A. Sz\'ekely}
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{\bf Towards a Katona Type Proof for the 2-intersecting \break
Erd\H os-Ko-Rado Theorem}
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We study the possibility of the existence of
a  Katona type proof for the
Erd\H os-Ko-Rado theorem for 2- and 3-intersecting families of sets.
 An Erd\H os-Ko-Rado type
theorem for 2-intersecting  integer arithmetic progressions and a model
theoretic argument show that such an approach works in the 2-intersecting
case, at least for some values of $n$ and $k$.


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