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Type
also called Complete type and has one more synonym

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  1. In model theory, a type is a set of first-order formulas in a language L with free variables x_1,x_2,\ldots,x_n which are true of a sequence of elements of an L-structure \mathcalA

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
  2. Consider a structure for a language L, or equivalently of a signature σ, M, a set of parameters A \subset M and some tuple of elements of M, \barb \in M^n

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
  3. of \barb over A is the set of all first-order σ-formulae \psi with free variables x_1,x_2,\ldots,x_n, and parameters in A which are satisfied by \barb

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
  4. For example, the complete type of the number 2 over the emptyset, considered as a member of the natural numbers, would be the list of all first-order statements describing a variable x that are true for x=2

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
  5. useful to consider the set of complete n-types over A as a topological space

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
  6. Given a complete n type p one can ask if there is a model of the theory that omits p, in other words there is no n-tuple of type p

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on December 8, 2008
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