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The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment.
Robinson's original approach was based on these nonstandard models of the field of real numbers. His classic foundational book on the subject Nonstandard Analysis was published in 1966 and is still in print. [8] On page 88, Robinson writes: The existence of nonstandard models of arithmetic was discovered by Thoralf Skolem (1934).
In model theory, a discipline within mathematical logic, a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard model). [ 1 ] Existence
The standard system of the model is the collection {:}. It can be shown that the standard system of any nonstandard model of PA contains a nonrecursive set, either by appealing to the incompleteness theorem or by directly considering a pair of recursively inseparable r.e. sets (Kaye 1991:154).
Institutional model theory. Institution (computer science) Non-standard analysis. Non-standard calculus; Hyperinteger; Hyperreal number; Transfer principle; Overspill; Elementary Calculus: An Infinitesimal Approach; Criticism of non-standard analysis; Standard part function; Set theory. Forcing (mathematics) Boolean-valued model; Kripke ...
These methods model their computational operations based on non-standard paradigms, and are currently mostly in the research and development stage. This computing behavior can be "simulated" [clarification needed] using classical silicon-based micro-transistors or solid state computing technologies, but it aims to achieve a new kind of computing.
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Sharable Content Object Reference Model (SCORM) is a collection of standards and specifications for web-based electronic educational technology (also called e-learning). It defines communications between client side content and a host system (called "the run-time environment"), which is commonly supported by a learning management system.