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Abstract Objects: An Introduction to Axiomatic Metaphysics is the title of a publication by Edward Zalta that outlines abstract object theory.
On Zalta's account, some objects (the ordinary concrete ones around us, like tables and chairs) "exemplify" properties, while others ("abstract objects like numbers, and what others would call "non-existent objects", like the round square, and the mountain made entirely of gold) merely "encode" them. While the objects that exemplify properties are discovered through traditional empirical means, a simple set of axioms allows us to know about objects that encode properties. For every set of properties, there is exactly one object that encodes exactly that set of properties and no others. This allows for a formalized "ontology.