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The Standard Model of particle physics is ... This is the only dimensional parameter of the Standard Model and has a measured value of ... a complete theory ...
has units of mass, and it is the only parameter in the Standard Model that is not dimensionless. It is also much smaller than the Planck scale and about twice the Higgs mass, setting the scale for the mass of all other particles in the Standard Model. This is the only real fine-tuning to a small nonzero value in the Standard Model.
The complete Standard Model requires 25 fundamental dimensionless constants (Baez, 2011). At present, their numerical values are not understood in terms of any widely accepted theory and are determined only from measurement. These 25 constants are: the fine structure constant; the strong coupling constant;
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Complete arithmetic (also known as true arithmetic) is the theory of the standard model of arithmetic, the natural numbers N. It is complete but does not have a recursively enumerable set of axioms. It is complete but does not have a recursively enumerable set of axioms.
A set is described by listing elements separated by commas, or by a characterizing property of its elements, within braces { }. [8] Since sets are objects, the membership relation can relate sets as well, i.e., sets themselves can be members of other sets. A derived binary relation between two sets is the subset relation, also called set inclusion.
A model completion for a theory T is a model companion T* such that for any model M of T, the theory of T* together with the diagram of M is complete. Roughly speaking, this means every model of T is embeddable in a model of T* in a unique way. If T* is a model companion of T then the following conditions are equivalent: [3] T* is a model ...
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