Sh:479
- Shelah, S. (1996). On Monk’s questions. Fund. Math., 151(1), 1–19. arXiv: math/9601218 MR: 1405517
-
Abstract:
Monk asks (problems 13, 15 in his list; is the algebraic density): "For a Boolean algebra , , does have a subalgebra with ?" If is regular the answer is easily positive, we show that in general it may be negative, but for quite many singular cardinals - it is positive; the theorems are quite complementary. Next we deal with and we show that the of an ultraproduct of Boolean algebras is not necessarily the ultraproduct of the ’s. We also prove that for infinite Boolean algebras () and a non-principal ultrafilter on : if for and is regular, then . Here . By a theorem of Peterson the regularity of is needed. - Version 1996-01-08_10 (22p) published version (19p)
Bib entry
@article{Sh:479, author = {Shelah, Saharon}, title = {{On Monk's questions}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {151}, number = {1}, year = {1996}, pages = {1--19}, issn = {0016-2736}, mrnumber = {1405517}, mrclass = {03E05 (03E35 03G05 04A20 06E05)}, note = {\href{https://arxiv.org/abs/math/9601218}{arXiv: math/9601218}}, arxiv_number = {math/9601218} }