# Prime Model

In mathematics, and in particular model theory, a prime model is a model which is as simple as possible. Specifically, a model is prime if it admits an elementary embedding into any model to which it is elementarily equivalent (that is, into any model satisfying the same complete theory as ).

### Other articles related to "prime model, prime, models, model":

Prime Model - Relationship With Saturated Models
... There is a duality between the definitions of prime and saturated models ... Half of this duality is discussed in the article on saturated models, while the other half is as follows ... While a saturated model realizes as many types as possible, a prime model realizes as few as possible it is an atomic model, realizing only the types which ...
September 13 - Births
2012) 1927 – Tzannis Tzannetakis, Greek politician, 175th Prime Minister of Greece (d ... Rabuka, Fijian revolutionary and politician, 3rd Prime Minister of Fiji 1949 – John W ... football player 1968 – Emma Wiklund, Swedish model and actress 1968 – Bernie Williams, Puerto Rican baseball player 1969 – Ilka Knickenberg, German actress 1969 – Tyler Perry, American actor ...
September 25 - Births
1764) 1694 – Henry Pelham, English politician, Prime Minister of the United Kingdom (d. 1793) 1766 – Armand-Emmanuel de Vignerot du Plessis, Duc de Richelieu, French politician, Prime Minister of France (d. 1897) 1862 – Billy Hughes, Australian politician, 7th Prime Minister of Australia (d ...
April 8 - Births
1919 – Ian Smith, Zimbabwean politician, 1st Prime Minister of Rhodesia (d. 1928 – Leah Rabin, Israeli widow of Prime Minister Yitzhak Rabin(d ... Secretary General 1938 – John Hamm, Canadian politician 1939 – Mary Leona Gage, American model and actress, Miss USA 1957 (d ...
Saturated Model - Relationship To Prime Models
... The notion of saturated model is dual to the notion of prime model in the following way let T be a countable theory in a first-order language (that is, a set of mutually consistent ... The equivalent notion for saturated models is that any "reasonably small" model of T is elementarily embedded in a saturated model, where "reasonably small" means cardinality no larger than ... Any saturated model is also homogeneous ...

### Famous quotes containing the words model and/or prime:

The Battle of Waterloo is a work of art with tension and drama with its unceasing change from hope to fear and back again, change which suddenly dissolves into a moment of extreme catastrophe, a model tragedy because the fate of Europe was determined within this individual fate.
Stefan Zweig (18811942)

Ay, look: high heaven and earth ail from the prime foundation;
All thoughts to rive the heart are here, and all are vain:
Horror and scorn and hate and fear and indignation—
Oh, why did I awake? When shall I sleep again?
—A.E. (Alfred Edward)