On the non-existence of $$\kappa $$-mad families
نویسندگان
چکیده
Starting from a model with Laver-indestructible supercompact cardinal $$\kappa $$ , we construct of $$ZF+DC_{\kappa }$$ where there are no -mad families.
منابع مشابه
on the effect of linear & non-linear texts on students comprehension and recalling
چکیده ندارد.
15 صفحه اولVery Mad Families
The notion of very mad family is a strengthening of the notion of mad family of functions. Here we show existence of very mad families in different contexts.
متن کاملMAD families and the rationals
Rational numbers are used to classify maximal almost disjoint (MAD) families of subsets of the integers. Combinatorial characterization of indestructibility of MAD families by the likes of Cohen, Miller and Sacks forcings are presented. Using these it is shown that Sacks indestructible MAD family exists in ZFC and that b = c implies that there is a Cohen indestructible MAD family. It follows th...
متن کاملForcing indestructibility of MAD families
Let A ⊆ [ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families wh...
متن کاملMad families, splitting families and large continuum
Let κ < λ be regular uncountable cardinals. Using a finite support iteration of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Archive for Mathematical Logic
سال: 2023
ISSN: ['1432-0665', '0933-5846']
DOI: https://doi.org/10.1007/s00153-023-00874-6