Geodesic
New Ramsey classes from old
Manuel Bodirsky1
1Ecole Polytechnique / CNRS
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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Let $\mathcal{C}_1$ and $\mathcal{C}_2$ be strong amalgamation classes of finite structures, with disjoint finite signatures $\sigma$ and $\tau$. Then $\mathcal{C}_1 \wedge \mathcal{C}_2$ denotes the class of all finite ($\sigma\cup\tau$)-structures whose $\sigma$-reduct is from $\mathcal{C}_1$ and whose $\tau$-reduct is from $\mathcal{C}_2$. We prove that when $\mathcal{C}_1$ and $\mathcal{C}_2$ are Ramsey, then $\mathcal{C}_1 \wedge \mathcal{C}_2$ is also Ramsey. We also discuss variations of this statement, and give several examples of new Ramsey classes derived from those general results.
DOI : 10.37236/2566
Classification : 05D10, 03C10, 22F50
Mots-clés : Ramsey classes, homogeneous structures, extreme amenability

Manuel Bodirsky  1

1 Ecole Polytechnique / CNRS 
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     author = {Manuel Bodirsky},
     title = {New {Ramsey} classes from old},
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     doi = {10.37236/2566},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/2566/}
}
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Manuel Bodirsky. New Ramsey classes from old. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/2566

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