Closed maximality principles: implications, separations and combinations
نویسندگان
چکیده
منابع مشابه
Closed maximality principles: implications, separations and combinations
I investigate versions of the Maximality Principles for the classes of forcings which are <κ-closed, <κ-directed-closed, or of the form Col(κ,< λ). These principles come in many variants, depending on the parameters which are allowed. I shall write MPΓ(A) for the maximality principle for forcings in Γ, with parameters from A. The main results of this paper are: • The principles have many conseq...
متن کاملOn certain maximality principles
We present streamlined proofs of certain maximality principles studied by Hamkins and Woodin. Moreover, we formulate an intermediate maximality principle, which is shown here to be equiconsistent with the existence of a weakly compact cardinal $kappa$ such that $V_{kappa}prec V$.
متن کاملConsistency Strengths of Modified Maximality Principles
The Maximality Principle mp is a scheme which states that if a sentence of the language of zfc is true in some forcing extension V , and remains true in any further forcing extension of V , then it is true in all forcing extensions of V . A modified maximality principle mpΓ arises when considering forcing with a particular class Γ of forcing notions. A parametrized form of such a principle, mpΓ...
متن کاملCombined Maximality Principles up to large cardinals
The motivation for this paper is the following: In [Fuc08] I showed that it is inconsistent with ZFC that the maximality principle for closed forcings holds at unboundedly many regular cardinals κ (even only allowing κ itself as a parameter in the maximality principle for <κ-closed forcings each time). So the question is whether it is consistent to have this principle at unboundedly many regula...
متن کاملOn a Class of Maximality Principles
We study various classes of maximality principles, MP(κ,Γ), introduced by J.D. Hamkins in [6], where Γ defines a class of forcing posets and κ is an infinite cardinal. We explore the consistency strength and the relationship of MP(κ,Γ) with various forcing axioms when κ ∈ {ω, ω1}. In particular, we give a characterization of bounded forcing axioms for a class of forcings Γ in terms of maximalit...
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: Journal of Symbolic Logic
سال: 2008
ISSN: 0022-4812,1943-5886
DOI: 10.2178/jsl/1208358754