Model-theoretic Properties
True arithmetic is an unstable theory, and so has models for each uncountable cardinal . As there are continuum many types over the empty set, true arithmetic also has countable models. Since the theory is complete, all of its models are elementarily equivalent.
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“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)