Much of mathematics, including Graph Theory, is built on the foundation of ZFC set theory. However there are other foundations and the choice of ZFC might be just a historical coincidence. In particular, ZFS foundation in many respects is "better" or as "good" as ZFC foundation: it allows a complete Lebesgue measure theory and hence analysis and physics might be built on ZFS foundation; but on the other hand it eliminates anomalies such as Banach-Tarsky paradox. The Shelah-Soifer class 5 of graphs illustrates how different mathematics could be if it were built on a different foundation. This provokes numerous questions, in particular: 1. What if we try to continue the Solovay's project and build analysis on top of ZFS? 2. How different this ZFS-analysis would be? 3. Would the physics from the point of .ZFS-analysis give better predictions?
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