Elementary submodels in infinite combinatorics

Details Elementary submodels in infinite combinatorics Elementary submodels in infinite combinatorics

2010-07-25

arxiv.org/abs/1007.4309v2

Mathematics

Logic

Scientific paper

The usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary submodels. We also present a new proof of Nash-Williams's theorem on cycle-decomposition of graphs, and finally we improve a decomposition theorem of Laviolette concerning bond-faithful decompositions of graphs.

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