Black Boxes

Details Black Boxes Black Boxes

2008-12-03

arxiv.org/abs/0812.0656v2

Mathematics

Logic

Scientific paper

We introduce Black Boxes, the intention being provably in ZFC, we have guesses of extra structure. The guesses are pairwise quite far but together are "dense". We first deal with the simplest case, were the existence comes from winning a game by just writing down the opponent's moves. We show how it helps when instead orders we have tress with boundedly many levels, having freedom in the last. After this we quite systematically look at existence of black boxes, and make connection to non-saturation of natural ideals and diamonds on them. Chapter IV of upcoming book "Nonstructure Theory".

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