Suslin Forcing and Parametrized ♦ Principles
نویسنده
چکیده
By using finite support iteration of Suslin c.c.c forcing notions we construct several models which satisfy some ♦-like principles while other cardinal invariants are
منابع مشابه
Preserving Non–Null with Suslin proper forcings
We (i.e. I) present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is the ideal generated by a Suslin ccc forcing (e.g. Lesbeque– null or meager), and P is a Suslin forcing, and P is I–preserving (i.e. it doesn’t make any positive Borel–set small), then P preserves generics over candidates and therefore is strongly I–preserving (i.e. doesn’t make any positi...
متن کاملar X iv : m at h / 04 05 08 1 v 1 [ m at h . L O ] 5 M ay 2 00 4 Preserving Preservation
We present preservation theorems for countable support iteration of nep forcing notions satisfying “old reals are not Lebesgue null” (section 6) and “old reals are not meager” (section 5). (Nep is a generalization of Suslin proper.) We also give some results for general Suslin ccc ideals (the results are summarized in a diagram on page 17). This paper is closely related to [She98, XVIII, §3] an...
متن کاملTopics in Set Theory
Axiomatics. The formal axiomatic system of ordinary set theory (ZFC). Models of set theory. Absoluteness. Simple independence results. Transfinite recursion. Ranks. Reflection principles. Constructibility. [4] Infinitary combinatorics. Cofinality. Stationary sets. Fodor’s lemma. Solovay’s theorem. Cardinal exponentiation. Beth and Gimel functions. Generalized Continuum Hypothesis. Singular Card...
متن کاملDominating Analytic Families
Let A be an analytic family of sequences of sets of integers. We show that either A is dominated or it contains a continuum of almost disjoint sequences. From this we obtain a theorem by Shelah that a Suslin c.c.c. forcing adds a Cohen real if it adds an unbounded real.
متن کاملOCA and towers in P ( N ) / fin
We shall show that Open Coloring Axiom has different influence on the algebra P(N)/fin than on N/fin. The tool used to accomplish this is forcing with a Suslin tree.
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 2007