sets - MathStructures

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=====Sets=====

Abbreviation: **Set**
====Definition====
A \emph{set} is a structure $\mathbf{A}=\langle A\rangle$ with no operations or relations defined on $A$.

==Morphisms==
Let $\mathbf{A}$ and $\mathbf{B}$ be sets. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$.

====Examples====
Example 1: 

====Basic results====


====Properties====
^[[Classtype]]  |  variety |
^[[Equational theory]]  |  decidable |
^[[Quasiequational theory]]  |  decidable |
^[[First-order theory]]  |  decidable |
^[[Locally finite]]  |  yes |
^[[Residual size]]  |  2 |
^[[Congruence distributive]]  |  no |
^[[Congruence modular]]  |  no |
^[[Congruence n-permutable]]  |  no |
^[[Congruence regular]]  |  no |
^[[Congruence uniform]]  |  no |
^[[Congruence extension property]]  |  yes |
^[[Definable principal congruences]]  |  yes |
^[[Equationally def. pr. cong.]]  |  no |
^[[Amalgamation property]]  |  yes |
^[[Strong amalgamation property]]  |  yes |
^[[Epimorphisms are surjective]]  |  yes |
====Finite members====

$\begin{array}{lr}
  f(n)= &1\\
\end{array}$

====Subclasses====
  [[One-element structures]] 

====Superclasses====

====References====

[(Ln19xx>
)]

Trace: • mv-algebras • rings • cancellative_semigroups • inverse_semigroups • quasigroups • bck-algebras • join-semidistributive_lattices • cancellative_partial_monoids • boolean_semigroups • complete_semilattices