Aronszajn lines and the club filter
نویسنده
چکیده
The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.
منابع مشابه
Dissertation Subject Oral Syllabus
(a) Definition of a ∆-system, statement and proof of the ∆-system lemma. (b) Statement of MA (Martin’s Axiom) and MAκ, proof that MAω holds and MAc fails. (c) Definition of a club and a stationary subset of κ, of the club filter and proof that the club filter on a regular cardinal κ is κ-complete. (d) Statement and proof of the Pressing Down Lemma. i. An application: Statement and proof of Thom...
متن کاملThin Stationary Sets and Disjoint Club Sequences
We describe two opposing combinatorial properties related to adding clubs to ω2: the existence of a thin stationary subset of Pω1 (ω2) and the existence of a disjoint club sequence on ω2. A special Aronszajn tree on ω2 implies there exists a thin stationary set. If there exists a disjoint club sequence, then there is no thin stationary set, and moreover there is a fat stationary subset of ω2 wh...
متن کاملUncountable Linear Orders
Two important classes of linear orders that are not σ-scattered are the real types and the Aronszajn types: the real types are those uncountable dense linear orders that are separable; the Aronszajn types are those linear orders that are uncountable and yet have no uncountable suborders that are scattered or real types. This latter class was considered—and proved nonempty—long ago by Aronszajn ...
متن کاملA Universal Aronszajn Line
The purpose of this note is to define an Aronszajn line ηC and prove that under the assumption of PFA it is universal for the class of Aronszajn lines. Moreover ηC can be easily described in terms of a fixed Countryman type C: it is the direct limit of the finite lexicographic products of the form C × (−C)× . . .× (±C).
متن کاملMiniaturized High-Pass Filter Based on Balanced Composite Right-Left Handed Transmission Line Using Meander Spiral Complementary Split Ring Resonators
In this paper, a compact high-pass filter (HPF) with a sharp rejection response based on the balanced composite right-left handed (CRLH) transmission line (TL) concept is proposed. A series LC resonator using an interdigital capacitor and meander lines is designed. Also, a meander spiral complementary split ring resonator (MSCSRR) is used to realize the parallel LC resonator. The high-pass filt...
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:
- J. Symb. Log.
دوره 73 شماره
صفحات -
تاریخ انتشار 2008