Sh:1172
- Kaplan, I., Segel, O., & Shelah, S. (2022). Boolean types in dependent theories. J. Symb. Log., 87(4), 1349–1373. arXiv: 2008.03214 DOI: 10.1017/jsl.2022.7 MR: 4510824
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Abstract:
The notion of a complete type can be generalized in a natural manner to allow assigning a value in an arbitrary Boolean algebra \mathcal{B} to each formula. We show some basic results regarding the effect of the properties of \mathcal{B} on the behavior of such types, and show they are particularity well behaved in the case of NIP theories. In particular, we generalize the third author’s result about counting types, as well as the notion of a smooth type and extending a type to a smooth one. We then show that Keisler measures are tied to certain Boolean types and show that some of the results can thus be transferred to measures — in particular, giving an alternative proof of the fact that every measure in a dependent theory can be extended to a smooth one. We also study the stable case. We consider this paper as an invitation for more research into the topic of Boolean types. - Version 2022-01-16 (32p) published version (25p)
Bib entry
@article{Sh:1172,
author = {Kaplan, Itay and Segel, Ori and Shelah, Saharon},
title = {{Boolean types in dependent theories}},
journal = {J. Symb. Log.},
fjournal = {The Journal of Symbolic Logic},
volume = {87},
number = {4},
year = {2022},
pages = {1349--1373},
issn = {0022-4812},
mrnumber = {4510824},
mrclass = {03C45 (03C95 03G05 28A60)},
doi = {10.1017/jsl.2022.7},
note = {\href{https://arxiv.org/abs/2008.03214}{arXiv: 2008.03214}},
arxiv_number = {2008.03214}
}