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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Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)