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 ).

Read more about Prime Model: Cardinality, Relationship With Saturated Models

### 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 ...

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 ...

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 ...

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 ...

**Prime Model**s

... 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)

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Horror and scorn and hate and fear and indignation—

Oh, why did I awake? When shall I sleep again?”

—A.E. (Alfred Edward)