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An approach to universal (meta-)logical reasoning in classical higher-order logic is employed to explore and study simplifications of Kurt G\"odel's modal ontological argument. Some argument premises are modified, others are dropped, modal collapse is avoided and validity is shown already in weak modal logics K and T. Key to the gained simplifications of G\"odel's original theory is the exploitation of a link to the notions of filter and ultrafilter from topology. The paper illustrates howarXiv:2001.04701v10 fatcat:biplwnjbd5fetmfdvt3pul2664