Zobrazeno 1 - 10
of 176
pro vyhledávání: '"GOLDSTERN, MARTIN"'
Publikováno v:
Israel Journal of Mathematics, volume 246, pages 73-129, 2021
We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretel
Externí odkaz:
http://arxiv.org/abs/2007.13500
Publikováno v:
Journal of Mathematical Logic (online ready), 2021
We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new ${<}\kappa$-sequences (for some regular $\kappa$). As an application, we show that consistently the following cardinal characteristics can be di
Externí odkaz:
http://arxiv.org/abs/2006.09826
Cicho\'n's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent that all ent
Externí odkaz:
http://arxiv.org/abs/1906.06608
Given a forcing notion $P$ that forces certain values to several classical cardinal characteristics of the reals, we show how we can compose $P$ with a collapse (of a cardinal $\lambda>\kappa$ to $\kappa$) such that the composition still forces the p
Externí odkaz:
http://arxiv.org/abs/1904.02617
Publikováno v:
Arch. Math. Logic 60 (3-4), 2021, 343-411
We reimplement the creature forcing construction used by Fischer et al. (arXiv:1402.0367) to separate Cicho\'{n}'s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction
Externí odkaz:
http://arxiv.org/abs/1808.01921
Publikováno v:
Fundamenta Mathematicae 252 (2021), 241-314
For a strongly inacessible cardinal $\kappa$, we investigate the relationships between the following ideals: - the ideal of meager sets in the ${<}\kappa$-box product topology - the ideal of "null" sets in the sense of [Sh:1004] (arXiv:1202.5799) - t
Externí odkaz:
http://arxiv.org/abs/1806.08583
Publikováno v:
Annals of Mathematics 190, no. 1 (2019): 113-43
Assuming four strongly compact cardinals, it is consistent that all entries in Cicho\'n's diagram are pairwise different, more specifically that \[ \aleph_1 < \mathrm{add}(\mathrm{null}) < \mathrm{cov}(\mathrm{null}) < \mathfrak{b} < \mathrm{non}(\ma
Externí odkaz:
http://arxiv.org/abs/1708.03691
Publikováno v:
Comment. Math. Univ. Carol. 61 (1), 2020, 21-26
Typically, set theorists reason about forcing constructions in the context of ZFC. We show that without AC, several simple properties of forcing posets fail to hold, one of which answers Miller's question from arXiv:0704.3998.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/1706.01708
Publikováno v:
Proc. Amer. Math. Soc. 144 (2016), 4025-4042
Using a finite support iteration of ccc forcings, we construct a model of $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})=\mathfrak{c}$.
Comment: Publication 1066 on
Comment: Publication 1066 on
Externí odkaz:
http://arxiv.org/abs/1504.04192
Publikováno v:
Arch. Math. Logic 56 (2017), no. 7--8, 1045--1103
We use a (countable support) creature construction to show that consistently \[ \mathfrak d=\aleph_1= \text{cov}(\text{NULL}) < \text{non}(\text{MEAGER}) < \text{non}(\text{NULL}) < \text{cof}(\text{NULL}) < 2^{\aleph_0}. \] The same method shows the
Externí odkaz:
http://arxiv.org/abs/1402.0367