A remark on the tree property in a choiceless context
نویسنده
چکیده
We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from the consistency of a proper class of supercompact cardinals. This extends earlier results due to the author showing that the consistency of the theory “ZF + ¬ACω + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” follows from hypotheses stronger in consistency strength than a supercompact limit of supercompact cardinals. A lower bound in consistency strength is provided by a result of Busche and Schindler, who showed that the consistency of the theory “ZF + Every successor cardinal is regular + Every limit cardinal is singular + Every successor cardinal satisfies the tree property” implies the consistency of AD. We begin by very briefly mentioning some of our conventions and terminology. As usual, for κ a regular cardinal, a κ-tree is a tree of height κ, all of whose levels have cardinality less than κ. κ satisfies the tree property if every κ-tree has a branch of length κ. A κ-tree not satisfying the tree ∗2000 Mathematics Subject Classifications: 03E25, 03E35, 03E45, 03E55. †
منابع مشابه
Studying impressive parameters on the performance of Persian probabilistic context free grammar parser
In linguistics, a tree bank is a parsed text corpus that annotates syntactic or semantic sentence structure. The exploitation of tree bank data has been important ever since the first large-scale tree bank, The Penn Treebank, was published. However, although originating in computational linguistics, the value of tree bank is becoming more widely appreciated in linguistics research as a whole. F...
متن کاملA remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane
In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.
متن کاملAn Investigation of the Relevancy between Turco-Mongol Mythologies and the Motif of Tree in the Demotte Shahnameh and Jami al-Tavarikh from a Cultural Semiotic Point of View
In the view of a wider audience, the interpretations of book paintings from the Demmote Shahnama have never been the subject of detailed semiotic studies. While Ferdowsi’s Shahnama is a literary context with axial attention to the lyricism that appeared in the Iranian pretext, Jami al-Tavarikh is basically a historic source in which the pictorial language of the Ilkhanid context remained the ...
متن کاملA short remark on the result of Jozsef Sandor
It is pointed out that, one of the results in the recently published article, ’On the Iyengar-Madhava Rao-Nanjundiah inequality and it’s hyperbolic version’ [3] by J´ozsef S´andor is logically incorrect and new corrected result with it’s proof is presented.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 50 شماره
صفحات -
تاریخ انتشار 2011