Compactness versus hugeness at successor cardinals

نویسندگان

چکیده

If [Formula: see text] is regular and text], then the existence of a weakly presaturated ideal on implies text]. This partially answers question Foreman Magidor about approachability As corollary, we show that if there such semiproper, CH holds. We also some barriers to getting tree property saturated simultaneously successor cardinal from conventional forcing methods.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Partition Relations for Successor Cardinals

This paper investigates the relations K+ --t (a): and its variants for uncountable cardinals K. First of all, the extensive literature in this area is reviewed. Then, some possibilities afforded by large cardinal hypotheses are derived, for example, if K is measurable, then K + + (K + K + 1, a): for every a < K +. Finally, the limitations imposed on provability in ZFC by L and by relative consi...

متن کامل

Successor Large Cardinals in Symmetric Extensions ∗

We give an exposition in modern language (and using partial orders) of Jech’s method for obtaining models where successor cardinals have large cardinal properties. In such models, the axiom of choice must necessarily fail. In particular, we show how, given any regular cardinal and a large cardinal of the requisite type above it, there is a symmetric extension of the universe in which the axiom ...

متن کامل

Successor of Singulars: Combinatorics and Not Collapsing Cardinals

On the one hand we deal with (< κ)-supported iterated forcing notions which are (Ê0, Ê1)-complete, have in mind problems on Whitehead groups, uniformizations and the general problem. We deal mainly with the caes of a successor of the singular cardinal. This continues [Sh 587]. On the other hand we deal with complimentary ZFC combinatorial results. I would like to thank Alice Leonhardt for the b...

متن کامل

Tree Property at Successor of a Singular Limit of Measurable Cardinals

Assume λ is a singular limit of η supercompact cardinals, where η ≤ λ is a limit ordinal. We present two forcing methods for making λ+ the successor of the limit of the first η measurable cardinals while the tree property holding at λ+. The first method is then used to get, from the same assumptions, tree property at אη2+1 with the failure of SCH at אη2 . This extends results of Neeman and Sina...

متن کامل

Equiconsistencies at subcompact cardinals

We present equiconsistency results at the level of subcompact cardinals. Assuming SBHδ, a special case of the Strategic Branches Hypothesis, we prove that if δ is a Woodin cardinal and both 2(δ) and 2δ fail, then δ is subcompact in a class inner model. If in addition 2(δ) fails, we prove that δ is Π21 subcompact in a class inner model. These results are optimal, and lead to equiconsistencies. A...

متن کامل

ذخیره 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: Journal of Mathematical Logic

سال: 2022

ISSN: ['0219-0613', '1793-6691']

DOI: https://doi.org/10.1142/s0219061322500167