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The development of the Standard Model was driven by theoretical and experimental particle physicists alike. The Standard Model is a paradigm of a quantum field theory for theorists, exhibiting a wide range of phenomena, including spontaneous symmetry breaking, anomalies, and non-perturbative behavior.
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.
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.
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The standard construction of the naturals, due to John von Neumann, starts from a definition of 0 as the empty set, ∅, and an operator s on sets defined as: = {} The set of natural numbers N is defined as the intersection of all sets closed under s that contain the empty set. Each natural number is equal (as a set) to the set of natural ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
A standard model M that satisfies the additional transitivity condition that x ∈ y ∈ M implies x ∈ M is a standard transitive model (or simply a transitive model). Usually, when one talks about a model M of set theory, it is assumed that M is a set model, i.e. the domain of M is a set in V.
The Standard Model of particle physics was finalized in the mid-1970s upon experimental confirmation of the existence of quarks.Subsequent discoveries of the top quark (1995), the tau neutrino (2000), and the Higgs boson (2013), gave the model further credence.