Lajos Soukup
Published 2010-07-25, updated 2010-12-06Version 2
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.
Davies-trees in infinite combinatorics
Infinite Combinatorics revisited in the absence of Axiom of Choice
Open and solved problems concerning polarized partition relations
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