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In the mathematical field of model theory, the elementary diagram of a structure is the set of all sentences with parameters from the structure that are true in the structure. It is also called the complete diagram.
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The elementary diagram of A is the set eldiagA of all first-order σ'-sentences that are satisfied by A or, equivalently, the complete (first-order) theory of the natural expansion of A to the signature σ'.
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First, one extends the signature by adding a new constant symbol for every element of M. The complete theory of M for the extended signature σ' is called the elementary diagram of M. In the next step one adds κ many new constant symbols to the signature and adds to the elementary diagram of M the sentences c ≠ c' for any two distinct new constant symbols c and c'. Using the compactness theorem, the resulting theory is easily seen to be consistent. Since its models must have cardinality at least κ, the downward part of this theorem guarantees the existence of a model N which has cardinality exactly κ. It contains an isomorphic copy of M as an elementary substructure.
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Let M be a structure in a first-order language L. An extended language L(M) is obtained by adding to L a constant symbol ca for every element a of M. The structure M can be viewed as an L(M) structure in which the symbols in L are interpreted as before, and each new constant ca is interpreted as the element a. The elementary diagram of M is the set of all L(M) sentences that are true in M (Marker 2002:44).
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Comparison of pictorial and schematic styles of circuit diagrams Common schematic diagram symbols (US symbols) TTL counter, a type of state machine A circuit diagram (electrical diagram, elementary diagram, electronic schematic) is a graphical representation of an electrical circuit. A pictorial circuit diagram uses simple images of components, while a schematic diagram shows the components and interconnections of the circuit using standardized symbolic representations. The presentation of the interconnections between circuit components in the schematic diagram does not necessarily correspond to the physical arrangements in the finished device.Circuit diagrams and component layouts Unlike a block diagram or layout diagram, a circuit diagram shows the actual electrical connections.
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