A note on the induced Ramsey theorem for spaces
Bryce Frederickson, Vojtech R\"odl, Marcelo Sales
TL;DR
This paper provides a simplified proof of the induced Ramsey theorem for vector spaces, originally established by Prömel, enhancing understanding of combinatorial properties in linear algebraic structures.
Contribution
It offers a more accessible proof of the induced Ramsey theorem for vector spaces, making the result easier to understand and apply.
Findings
Simplified proof of the induced Ramsey theorem for vector spaces
Clarification of combinatorial properties in linear algebraic structures
Potential for broader application in related combinatorial problems
Abstract
The aim of this note is to give a simplified proof of the induced version of the Ramsey theorem for vector spaces first proved by H. J. Pr\"{o}mel.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Advanced Banach Space Theory · Optimization and Variational Analysis