Axiom 1: If φ is a positive property, and if it is necessarily true (true in all possible worlds) that every object with property φ also has property ψ, then ψ is also a positive property. Axiom 2: The negation of a property φ is positive if, and only if, φ is not positive. Theorem 1: If a property φ is positive, then it is possible that there exists an object x that has this property (in at least one possible world, there exists an object x that has this property). Definition 1: An object x is God-like if, and only if, x has all positive properties. Axiom 3: The property of being God-like is itself a positive property. Theorem 2: It is possible that there exists a God-like object x (in at least one possible world, there exists a God-like object x). Definition 2: A property φ is an essential property of an object x if, x has property φ, and every property ψ of x necessarily (in all possible worlds) and generally (for all objects) follows from φ. Axiom 4: If a property φ is positive, then it is necessarily positive (positive in all possible worlds). Theorem 3: If x is God-like, then being God-like is an essential property of x. Definition 3: An object x "exists necessarily" if each of its essential properties φ applies, in each possible world, to some object y. Axiom 5: "Necessary existence" is a positive property. Theorem 4: It is necessarily true (true in all possible worlds) that a God-like object exists.

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