On the Consistency Strength of `Accessible' Jonsson Cardinals and of the Weak Chang Conjecture.

1989 ◽  
Vol 54 (4) ◽  
pp. 1496
Author(s):  
Sy D. Friedman ◽  
Hans-Dieter Donder ◽  
Peter Koepke ◽  
Peter Koepke
Keyword(s):  
Consistency Strength ◽  
Jonsson Cardinals

scholarly journals E-cigarette Use and Respiratory Disorder: An Integrative Review of Converging Evidence from Epidemiological and Laboratory Studies

2020 ◽  
pp. 1901815
Author(s):  
Thomas A. Wills ◽  
Samir S. Soneji ◽  
Kelvin Choi ◽  
Ilona Jaspers ◽  
Elizabeth K. Tam
Keyword(s):  
Electronic Cigarettes ◽  
Meta Analysis ◽  
Epidemiological Studies ◽  
Chronic Obstructive ◽  
Human Populations ◽  
Respiratory Disorder ◽  
Biological Processes ◽  
Cigarette Use ◽  
Laboratory Studies ◽  
Consistency Strength

BackgroundUse of electronic cigarettes (e-cigarettes) is prevalent among adolescents and young adults but there has been limited knowledge about health consequences in human populations. We conduct a systematic review and meta-analysis of results on respiratory disorder from studies of general-population samples and consider the mapping of these results to findings about biological processes linked to e-cigarettes in controlled laboratory studies.MethodWe conduct a literature search and meta-analysis of epidemiological studies on the association of e-cigarette use with asthma and with chronic obstructive pulmonary disease (COPD). We then discuss findings from laboratory studies about effects of e-cigarettes on four biological processes: cytotoxicity, oxidative stress/inflammation, susceptibility to infection, and genetic expression.ResultsEpidemiological studies, both cross-sectional and longitudinal, show a significant association of e-cigarette use with asthma and COPD, controlling for cigarette smoking and other covariates. For asthma (n=15 studies), the pooled adjusted odds ratio (AOR) was 1.39 (CI 1.28–1.51); for COPD (n=9 studies) the AOR was 1.49 (CI 1.36–1.65). Laboratory studies consistently show an effect of e-cigarettes on biological processes related to respiratory harm and susceptibility to illness, with e-cigarette conditions differing significantly from clean-air controls though sometimes less than for cigarettes.ConclusionsThe evidence from epidemiological studies meets established criteria for consistency, strength of effect, temporality, and in some cases a dose-response gradient. Biological plausibility is indicated by evidence from multiple laboratory studies. We conclude that e-cigarette use has consequences for asthma and COPD, which is of significant concern for respirology and public health.

An AD-like model

1985 ◽  
Vol 50 (2) ◽  
pp. 531-543 ◽  
Author(s):  
Arthur W. Apter
Keyword(s):  
Measurable Cardinal ◽  
Large Cardinals ◽  
Strong Sense ◽  
Supercompact Cardinals ◽  
Singular Cardinals ◽  
Partial Orderings ◽  
Measurable Cardinals ◽  
Jonsson Cardinals

A very fruitful line of research in recent years has been the application of techniques in large cardinals and forcing to the production of models in which certain consequences of the axiom of determinateness (AD) are true or in which certain “AD-like” consequences are true. Numerous results have been published on this subject, among them the papers of Bull and Kleinberg [4], Bull [3], Woodin [15], Mitchell [11], and [1], [2].Another such model will be constructed in this paper. Specifically, the following theorem is proven.Theorem 1. Con(ZFC + There are cardinals κ < δ < λ so that κ is a supercompact limit of supercompact cardinals, λ is a measurable cardinal, and δ is λ supercompact) ⇒ Con(ZF + ℵ1 and ℵ2 are Ramsey cardinals + The ℵn for 3 ≤ n ≤ ω are singular cardinals of cofinality ω each of which carries a Rowbottom filter + ℵω + 1 is a Ramsey cardinal + ℵω + 2 is a measurable cardinal).It is well known that under AD + DC, ℵ2 and ℵ2 are measurable cardinals, the ℵn for 3 ≤ n < ω are singular Jonsson cardinals of cofinality ℵ2, ℵω is a Rowbottom cardinal, and ℵω + 1 and ℵω + 2 are measurable cardinals.The proof of the above theorem will use the existence of normal ultrafilters which satisfy a certain property (*) (to be defined later) and an automorphism argument which draws upon the techniques developed in [9], [2], and [4] but which shows in addition that certain supercompact Prikry partial orderings are in a strong sense “homogeneous”. Before beginning the proof of the theorem, however, we briefly mention some preliminaries.

scholarly journals THE CONSISTENCY STRENGTH OF LONG PROJECTIVE DETERMINACY

2019 ◽  
Vol 85 (1) ◽  
pp. 338-366 ◽  
Author(s):  
JUAN P. AGUILERA ◽  
SANDRA MÜLLER
Keyword(s):  
Set Theory ◽  
Consistency Strength ◽  
Axiom Of Determinacy ◽  
Woodin Cardinals ◽  
Inner Model ◽  
Image Position ◽  
Woodin Cardinal

AbstractWe determine the consistency strength of determinacy for projective games of length ω2. Our main theorem is that $\Pi _{n + 1}^1 $-determinacy for games of length ω2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that Mn (A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $$A = R$$ and the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this.We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω2 with payoff in $^R R\Pi _1^1 $ or with σ-projective payoff.

scholarly journals SQUARES, ASCENT PATHS, AND CHAIN CONDITIONS

2018 ◽  
Vol 83 (04) ◽  
pp. 1512-1538 ◽  
Author(s):  
CHRIS LAMBIE-HANSON ◽  
PHILIPP LÜCKE
Keyword(s):  
Partial Order ◽  
Set Theory ◽  
Consistency Strength ◽  
Chain Conditions ◽  
Regular Cardinals ◽  
Aronszajn Tree ◽  
Square Principles ◽  
Image Position ◽  
Aronszajn Trees ◽  
Consistency Strengths

AbstractWith the help of various square principles, we obtain results concerning the consistency strength of several statements about trees containing ascent paths, special trees, and strong chain conditions. Building on a result that shows that Todorčević’s principle $\square \left( {\kappa ,\lambda } \right)$ implies an indexed version of $\square \left( {\kappa ,\lambda } \right)$, we show that for all infinite, regular cardinals $\lambda < \kappa$, the principle $\square \left( \kappa \right)$ implies the existence of a κ-Aronszajn tree containing a λ-ascent path. We then provide a complete picture of the consistency strengths of statements relating the interactions of trees with ascent paths and special trees. As a part of this analysis, we construct a model of set theory in which ${\aleph _2}$-Aronszajn trees exist and all such trees contain ${\aleph _0}$-ascent paths. Finally, we use our techniques to show that the assumption that the κ-Knaster property is countably productive and the assumption that every κ-Knaster partial order is κ-stationarily layered both imply the failure of $\square \left( \kappa \right)$.

DETERMINACY AND JÓNSSON CARDINALS INL(ℝ)

2014 ◽  
Vol 79 (4) ◽  
pp. 1184-1198 ◽  
Author(s):  
S. JACKSON ◽  
R. KETCHERSID ◽  
F. SCHLUTZENBERG ◽  
W. H. WOODIN
Keyword(s):  
Uncountable Cardinal ◽  
Jonsson Cardinals

AbstractAssume ZF + AD +V=L(ℝ) and letκ< Θ be an uncountable cardinal. We show thatκis Jónsson, and that if cof (κ) = ω thenκis Rowbottom. We also establish some other partition properties.

scholarly journals Ramsey-like cardinals II

2011 ◽  
Vol 76 (2) ◽  
pp. 541-560 ◽  
Author(s):  
Victoria Gitman ◽  
P. D. Welch
Keyword(s):  
Upper Bound ◽  
Large Cardinals ◽  
Large Cardinal ◽  
Core Model ◽  
Consistency Strength ◽  
The Core ◽  
Countable Ordinal ◽  
Elementary Embeddings ◽  
Remarkable Cardinals

AbstractThis paper continues the study of the Ramsey-like large cardinals introduced in [5] and [14]. Ramsey-like cardinals are defined by generalizing the characterization of Ramsey cardinals via the existence of elementary embeddings. Ultrafilters derived from such embeddings are fully iterable and so it is natural to ask about large cardinal notions asserting the existence of ultrafilters allowing only α-many iterations for some countable ordinal α. Here we study such α-iterable cardinals. We show that the α-iterable cardinals form a strict hierarchy for α ≤ ω1, that they are downward absolute to L for , and that the consistency strength of Schindler's remarkable cardinals is strictly between 1-iterable and 2-iterable cardinals.We show that the strongly Ramsey and super Ramsey cardinals from [5] are downward absolute to the core model K. Finally, we use a forcing argument from a strongly Ramsey cardinal to separate the notions of Ramsey and virtually Ramsey cardinals. These were introduced in [14] as an upper bound on the consistency strength of the Intermediate Chang's Conjecture.

□ on the singular cardinals

2008 ◽  
Vol 73 (4) ◽  
pp. 1307-1314
Author(s):  
James Cummings ◽  
Sy-David Friedman
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Consistency Strength ◽  
Combinatorial Principle ◽  
Singular Cardinals

AbstractWe give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen. Square on singular cardinals.

scholarly journals Cardinal preserving ideals

1999 ◽  
Vol 64 (4) ◽  
pp. 1527-1551 ◽  
Author(s):  
Moti Gitik ◽  
Saharon Shelah
Keyword(s):  
Consistency Strength ◽  
Normal Ideals

AbstractWe give some general criteria, when κ-complete forcing preserves largeness properties—like κ-presaturation of normal ideals on λ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength “NSλ is αi-preserving”, for λ > α2.

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