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Iterated Forcing with ${}^{\omega}\omega$bounding and Semiproper Preorders
"... Assume the Continuum Hypothesis (CH) in the ground model. If we iteratively force with preorders which are $\omega\omega$bounding and semiproper taking suitable limits, then so is the final preorder constructed. Therefore we may show that the Cofinal Branch Principle (CBP) of [F] is strictly weaker ..."
THE PROPER AND SEMIPROPER FORCING AXIOMS FOR FORCING NOTIONS THAT PRESERVE ℵ2 OR ℵ3
, 2008
"... We prove that the PFA lottery preparation of a strongly unfoldable cardinal κ under ¬0 ♯ forces PFA(ℵ2preserving), PFA(ℵ3preserving) and PFAℵ2,with2ω = κ = ℵ2. The method adapts to semiproper forcing, giving SPFA(ℵ2preserving), SPFA(ℵ3preserving) and SPFAℵ2 from the same hypothesis. It follows ..."
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Cited by 2 (1 self)
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We prove that the PFA lottery preparation of a strongly unfoldable cardinal κ under ¬0 ♯ forces PFA(ℵ2preserving), PFA(ℵ3preserving) and PFAℵ2,with2ω = κ = ℵ2. The method adapts to semiproper forcing, giving SPFA(ℵ2preserving), SPFA(ℵ3preserving) and SPFAℵ2 from the same hypothesis
Bounded Martin’s Maximum is stronger than the Bounded Semiproper Forcing Axiom
, 2003
"... We show that if Bounded Martin’s Maximum (BMM) holds then for every X ∈ V there is an inner model with a strong cardinal containing X. In particular, by [1], BMM is strictly stronger consistencywise than the Bounded SemiProper Forcing Axiom (BSPFA). 1 Introduction. Shelah has shown that the SemiP ..."
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Cited by 1 (0 self)
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We show that if Bounded Martin’s Maximum (BMM) holds then for every X ∈ V there is an inner model with a strong cardinal containing X. In particular, by [1], BMM is strictly stronger consistencywise than the Bounded SemiProper Forcing Axiom (BSPFA). 1 Introduction. Shelah has shown that the SemiProper
Bounded Martin's Maximum, weak Erdös cardinals, and ...
 J. SYMBOLIC LOGIC
, 2002
"... We prove that a form of the Erdös property (of consistency strength strictly weaker than the Weak Chang's Conjecture at !1 ), together with Bounded Martin's Maximum implies that Woodin's principle AC holds, and therefore 2 @ 0 = @2 . We also prove that AC implies that every func ..."
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Cited by 8 (2 self)
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function f : !1 ! !1 is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum fails.
HIERARCHIES OF FORCING AXIOMS I ITAY NEEMAN AND ERNEST SCHIMMERLING
"... Abstract. We prove new upper bound theorems on the consistency strengths of SPFA(θ), SPFA(θlinked) and SPFA(θ +cc). Our results are in terms of (θ,Γ)subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γindescribability. Our upper bound for SPFA( ..."
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that is (κ +,Σ 2 2)subcompact, which is also strictly weaker than κ +supercompact. 1. Getting started To better understand the Semiproper Forcing Axiom (SPFA) we break up SPFA into SPFA(C) for various classes C, where SPFA(C) is the statement that for all P ∈ C, if P is semiproper poset and D is a family
HIERARCHIES OF FORCING AXIOMS I ITAY NEEMAN AND ERNEST SCHIMMERLING
"... Abstract. We prove new upper bound theorems on the consistency strengths of SPFA(θ), SPFA(θlinked) and SPFA(θ +cc). Our results are in terms of (θ, Γ)subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γindescribability. Our upper bound for SPFA ..."
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.c.) is a cardinal κ that is (κ +, Σ 2 2)subcompact, which is also strictly weaker than κ +supercompact. 1. Getting started To understand the Semiproper Forcing Axiom (SPFA) better we break up SPFA into SPFA(C) for various classes C, where SPFA(C) is the statement that for all P ∈ C, if P is semiproper
A weak reflection compatible with tail club guessing via semiproper iteration
, 2007
"... A weak reflection compatible with tail club guessing via semiproper iteration(The interplay between set theory of the reals and iterated forcing) ..."
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A weak reflection compatible with tail club guessing via semiproper iteration(The interplay between set theory of the reals and iterated forcing)
The proper forcing axiom
 Proceedings of the ICM 2010
"... The author’s preparation of this article and his travel to the 2010 meeting of ..."
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Cited by 9 (1 self)
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The author’s preparation of this article and his travel to the 2010 meeting of
The ground axiom
 J. Symbolic Logic
"... Abstract. A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is firstorder expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many w ..."
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Cited by 14 (2 self)
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Abstract. A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set forcing extension of any inner model. The Ground Axiom is firstorder expressible, and any model of zfc has a class forcing extension which satisfies it. The Ground Axiom is independent of many
Results 1  10
of
269