Sh:309
- Shelah, S. (2022). Black boxes. Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 65, 69–130. arXiv: 0812.0656 MR: 4636538
Ch. IV of The Non-Structure Theory" book [Sh:e] -
Abstract:
We shall deal comprehensively with Black Boxes, the intention being that provably in ZFC we have a sequence of guesses of extra structure on small subsets, the guesses are pairwise with quite little interaction, are 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 help when instead orders we have trees 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. - Version 2023-04-26 (47p) published version (62p)
Bib entry
@article{Sh:309,
author = {Shelah, Saharon},
title = {{Black boxes}},
journal = {Ann. Univ. Sci. Budapest. E\"{o}tv\"{o}s Sect. Math.},
fjournal = {Annales Universitatis Scientiarum Budapestinensis de Rolando E\"{o}tv\"{o}s Nominatae. Sectio Mathematica},
volume = {65},
year = {2022},
pages = {69--130},
issn = {0524-9007},
mrnumber = {4636538},
mrclass = {03E05 (03C45 03C55)},
note = {\href{https://arxiv.org/abs/0812.0656}{arXiv: 0812.0656} Ch. IV of The Non-Structure Theory" book [Sh:e]},
arxiv_number = {0812.0656},
refers_to_entry = {Ch. IV of The Non-Structure Theory" book [Sh:e]}
}