Notions around tree property 1
نویسندگان
چکیده
منابع مشابه
Notions around the Tree Property 1
In this paper, we study the notions related to the tree property 1 (=TP1) or equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k-TP1. Then we introduce the notions of weak k-TP1 for k ≥ 2, and also supply type-counting criteria for those. We do not know whether weak k-TP1 implies TP1, but at least we prove that each weak k-TP1 impl...
متن کاملThe Tree Property up to אω+1
Assuming ω supercompact cardinals we force to obtain a model where the tree property holds both at אω+1, and at אn for all 2 ≤ n < ω. A model with the former was obtained by Magidor–Shelah from a huge cardinal and ω supercompact cardinals above it, and recently by Sinapova from ω supercompact cardinals. A model with the latter was obtained by Cummings–Foreman from ω supercompact cardinals. Our ...
متن کاملThe tree property at ℵω+1
We show that given ω many supercompact cardinals, there is a generic extension in which there are no Aronszajn trees at אω+1. This is an improvement of the large cardinal assumptions. The previous hypothesis was a huge cardinal and ω many supercompact cardinals above it, in Magidor-Shelah [7].
متن کاملAround Kolmogorov complexity: basic notions and results
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory [4, 1, 5, 2, 7] where one can find the detailed exposition of many difficult results as well as historical references. However, it seems that a short survey of its basi...
متن کاملPeriodic Temporal Notions as ‘Tree Partitionings’
The key notion for modelling calendar systems and many other periodic temporal notion is the mathematical concept of a partitioning of the real numbers. A partitioning of R splits the time axis into a sequence of intervals. Basic time units like seconds, minutes, hours, days, weeks, months, years etc. can all be represented as partitionings of R with finite partitions. Besides the basic time un...
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: Annals of Pure and Applied Logic
سال: 2011
ISSN: 0168-0072
DOI: 10.1016/j.apal.2011.02.001