Lusin sequences under CH and under Martin ’ s Axiom ∗
نویسندگان
چکیده
Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences. 2000 Mathematics Subject Classification . 03E05 (Combinatorial set theory), 03E50 (Continuum hypothesis and Martin’s axiom), 03E35 ( Consistency and independence results).
منابع مشابه
m at h . L O ] 1 5 Ju l 1 99 8 Lusin sequences under CH and under Martin ’ s Axiom ∗
Assuming the continuum hypothesis there is an inseparable sequence of length ω1 that contains no Lusin subsequence, while if Martin’s Axiom and ¬CH is assumed then every inseparable sequence (of length ω1) is a union of countably many Lusin subsequences.
متن کاملU-Lusin Sets in Hyperfinite Time Lines
In an !1{saturated nonstandard universe a cut is an initial segment of the hyperintegers, which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U , a corresponding U{topology on the hyperintegers by letting O be U open if for any x 2 O there is a y greater than all the elements in U such that the interval [x y; x+y] O. Let U be a cut in a hypernite time line H,...
متن کاملCost Efficiency Evaluation via Data Envelopment Analysis Approach for Undesirable Outputs based on the Weak Disposability Axiom (Case Study: 56 Electricity Producing Thermal Power Plants in Iran)
Cost efficiency evaluation is a very important and applicable issue in Data Envelopment Analysis (DEA). In this paper, the classical cost efficiency model in which all the input prices are known and fixed for each decision making unit is developed via undesirable outputs with the weak disposability axiom. The proposed model is a nonlinear model under the variable returns to scale condition,...
متن کاملOn a Theorem of Banach and Kuratowski and K-lusin Sets
In a paper of 1929, Banach and Kuratowski proved—assuming the continuum hypothesis—a combinatorial theorem which implies that there is no nonvanishing σ-additive finite measure μ on R which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size 20 and that the existence of such sets is independent of ZFC + ¬CH.
متن کاملSticks and Clubs
We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin’s Axiom for counta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003