amalgamation property

A class of $L$ -structures $S$ has the amalgamation property if and only ifwhenever $A,B_{1},B_{2}\\in S$ and $f_{i}:A\\rightarrow B_{i}$ are elementary embeddingsfor $i\\in\\{1,2\\}$ then there is some $C\\in S$ and some elementary embeddings $g_{i}:B_{i}\\rightarrow C$ for $i\\in\\{1,2\\}$ so that $g_{1}(f_{1}(x))=g_{2}(f_{2}(x))$ for all $x\\in A$ . That is, the following diagram commutes.

\\xymatrix{&{A}\\ar[dl]_{f_{1}}\\ar[dr]^{f_{2}}&\\\\{B_{1}}\\ar[dr]_{g_{1}}&&{B_{2}}\\ar[dl]^{g_{2}}\\\\&{C}&}

Compare this with the free product with amalgamated subgroup for groups andthe definition of pushout there.

随便看

ContinuityOfCompositionOfFunctions
continuity of composition of functions
ContinuityOfConvexFunctions
continuity of convex functions
ContinuityOfConvexFunctionsAlternateProof
continuity of convex functions, alternate proof
ContinuityOfNaturalPower
continuity of natural power
ContinuityOfSineAndCosine
continuity of sine and cosine
Continuous
continuous
ContinuousAlmostEverywhereVersusEqualToAContinuousFunctionAlmostEverywhere
continuous almost everywhere versus equal to a continuous function almost everywhere
ContinuousConvergence
continuous convergence
ContinuousDensityFunction
continuous density function
ContinuousDerivativeImpliesBoundedVariation
continuous derivative implies bounded variation
ContinuousEpimorphismOfCompactGroupsPreservesHaarMeasure
continuous epimorphism of compact groups preserves Haar measure
ContinuousFunctionalCalculus
continuous functional calculus
ContinuousFunctionsAreRiemannIntegrable

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