scholarly journals Closed maximality principles: implications, separations and combinations

2008 ◽  
Vol 73 (1) ◽  
pp. 276-308 ◽  
Author(s):  
Gunter Fuchs
Keyword(s):  
Equivalence Relation ◽  
Regular Cardinal ◽  
Highly Sensitive ◽  
Souslin Trees ◽  
Maximality Principles ◽  
Automorphism Tower

AbstractI 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 consequences, such as <κ-closed-generic (Hκ) absoluteness, and imply, e.g., that ◊κ holds. I give an application to the automorphism tower problem, showing that there are Souslin trees which are able to realize any equivalence relation, and hence that there are groups whose automorphism tower is highly sensitive to forcing.• The principles can be separated into a hierarchy which is strict, for many κ.• Some of the principles can be combined, in the sense that they can hold at many different κ simultaneously.The possibilities of combining the principles are limited, though: While it is consistent that MP<κ-closed(Hκ +) holds at all regular κ below any fixed α, the “global” maximality principle, stating that MP<κ-closed (Hκ ∪ {κ} ) holds at every regular κ, is inconsistent. In contrast to this, it is equiconsistent with ZFC that the maximality principle for directed-closed forcings without any parameters holds at every regular cardinal. It is also consistent that every local statement with parameters from Hκ⊦ that's provably <κ-closed-forceably necessary is true, for all regular κ.

Constructible lattices of c-degrees

1982 ◽  
Vol 47 (4) ◽  
pp. 739-754
Author(s):  
C.P. Farrington
Keyword(s):  
Set Theory ◽  
Regular Cardinal ◽  
Boolean Algebras ◽  
Combinatorial Complexity ◽  
Generic Extension ◽  
Transitive Model ◽  
Perfect Set ◽  
Consistency Results ◽  
Combinatorial Principles ◽  
Souslin Trees

This paper is devoted to the proof of the following theorem.Theorem. Let M be a countable standard transitive model of ZF + V = L, and let ℒ Є M be a wellfounded lattice in M, with top and bottom. Let ∣ℒ∣M = λ, and suppose κ ≥ λ is a regular cardinal in M. Then there is a generic extension N of M such that(i) N and M have the same cardinals, and κN ⊂ M;(ii) the c-degrees of sets of ordinals of N form a pattern isomorphic to ℒ;(iii) if A ⊂ On and A Є N, there is B Є P(κ+)N such that L(A) = L(B).The proof proceeds by forcing with Souslin trees, and relies heavily on techniques developed by Jech. In [5] he uses these techniques to construct simple Boolean algebras in L, and in [6] he uses them to construct a model of set theory whose c-degrees have orderlype 1 + ω*.The proof also draws on ideas of Adamovicz. In [1]–[3] she obtains consistency results concerning the possible patterns of c-degrees of sets of ordinals using perfect set forcing and symmetric models. These methods have the advantage of yielding real degrees, but involve greater combinatorial complexity, in particular the use of ‘sequential representations’ of lattices.The advantage of the approach using Souslin trees is twofold: first, we can make use of ready-made combinatorial principles which hold in L, and secondly, the notion of genericity over a Souslin tree is particularly simple.

scholarly journals Combined Maximality Principles up to large cardinals

2009 ◽  
Vol 74 (3) ◽  
pp. 1015-1046 ◽  
Author(s):  
Gunter Fuchs
Keyword(s):  
Regular Cardinal ◽  
Large Cardinals ◽  
Large Cardinal ◽  
Consistency Strength ◽  
Regular Cardinals ◽  
Maximality Principles

AbstractThe motivation for this paper is the following: In [4] I showed that it is inconsistent with ZFC that the Maximality Principle for directed 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 regular cardinals or at every regular cardinal below some large cardinal κ (instead of ∞), and if so, how strong it is. It turns out that it is consistent in many cases, but the consistency strength is quite high.

SQUARE WITH BUILT-IN DIAMOND-PLUS

2017 ◽  
Vol 82 (3) ◽  
pp. 809-833 ◽  
Author(s):  
ASSAF RINOT ◽  
RALF SCHINDLER
Keyword(s):  
Regular Cardinal ◽  
Infinite Cardinal ◽  
List Type ◽  
Type Number ◽  
Aronszajn Tree ◽  
Combinatorial Principles ◽  
Souslin Trees ◽  
Diamond Principle

AbstractWe formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds inLfor every infinite cardinal.As an application, we prove that the following two hold inL:1.For every infinite regular cardinalλ, there exists a special λ+-Aronszajn tree whose projection is almost Souslin;2.For every infinite cardinalλ, there exists arespectingλ+-Kurepa tree; Roughly speaking, this means that this λ+-Kurepa tree looks very much like the λ+-Souslin trees that Jensen constructed inL.

scholarly journals Degrees of rigidity for Souslin trees

2009 ◽  
Vol 74 (2) ◽  
pp. 423-454 ◽  
Author(s):  
Gunter Fuchs ◽  
Joel David Hamkins
Keyword(s):  
Group Theory ◽  
Souslin Trees ◽  
Automorphism Tower

AbstractWe investigate various strong notions of rigidity for Souslin trees, separating them under ⟡ into a hierarchy. Applying our methods to the automorphism tower problem in group theory, we show under ⟡ that there is a group whose automorphism tower is highly malleable by forcing.

Ovarian Dysfunction in Fetally Irradiated Beagles

1977 ◽  
Vol 35 ◽  
pp. 658-659
Author(s):  
T. M. Seed ◽  
M. H. Sanderson ◽  
D. L. Gutzeit ◽  
T. E. Fritz ◽  
D. V. Tolle ◽  
...  
Keyword(s):  
Gamma Rays ◽  
Low Dose ◽  
Long Term Effects ◽  
Ovarian Dysfunction ◽  
Dose Rates ◽  
Highly Sensitive ◽  
Microscopic Evaluation ◽  
Ovarian Pathology ◽  
Normal Offspring

The developing mammalian fetus is thought to be highly sensitive to ionizing radiation. However, dose, dose-rate relationships are not well established, especially the long term effects of protracted, low-dose exposure. A previous report (1) has indicated that bred beagle bitches exposed to daily doses of 5 to 35 R 60Co gamma rays throughout gestation can produce viable, seemingly normal offspring. Puppies irradiated in utero are distinguishable from controls only by their smaller size, dental abnormalities, and, in adulthood, by their inability to bear young.We report here our preliminary microscopic evaluation of ovarian pathology in young pups continuously irradiated throughout gestation at daily (22 h/day) dose rates of either 0.4, 1.0, 2.5, or 5.0 R/day of gamma rays from an attenuated 60Co source. Pups from non-irradiated bitches served as controls. Experimental animals were evaluated clinically and hematologically (control + 5.0 R/day pups) at regular intervals.

Fluorescence ratio imaging of dynamic intracellular ionic signals

1988 ◽  
Vol 46 ◽  
pp. 42-43
Author(s):  
R. Y. Tsien ◽  
A. Minta ◽  
M. Poenie ◽  
J.P.Y. Kao ◽  
A. Harootunian
Keyword(s):  
Binding Sites ◽  
Living Cells ◽  
Molecular Engineering ◽  
Ph Indicators ◽  
Highly Sensitive ◽  
Fluorescence Ratio Imaging ◽  
Ratio Imaging ◽  
Technical Advances ◽  
Indicator Dyes ◽  
Fluorescein Dyes

Recent technical advances now enable the continuous imaging of important ionic signals inside individual living cells with micron spatial resolution and subsecond time resolution. This methodology relies on the molecular engineering of indicator dyes whose fluorescence is strong and highly sensitive to ions such as Ca2+, H+, or Na+, or Mg2+. The Ca2+ indicators, exemplified by fura-2 and indo-1, derive their high affinity (Kd near 200 nM) and selectivity for Ca2+ to a versatile tetracarboxylate binding site3 modeled on and isosteric with the well known chelator EGTA. The most commonly used pH indicators are fluorescein dyes (such as BCECF) modified to adjust their pKa's and improve their retention inside cells. Na+ indicators are crown ethers with cavity sizes chosen to select Na+ over K+: Mg2+ indicators use tricarboxylate binding sites truncated from those of the Ca2+ chelators, resulting in a more compact arrangement of carboxylates to suit the smaller ion.

Various technic for the measurement of step thickness on crystal surfaces

1978 ◽  
Vol 36 (1) ◽  
pp. 438-439
Author(s):  
C. Boulesteix ◽  
C. Colliex ◽  
C. Mory ◽  
B. Pardo ◽  
D. Renard
Keyword(s):  
Critical Thickness ◽  
Symmetric Case ◽  
Transmitted Intensity ◽  
Crystal Surfaces ◽  
Bright Field ◽  
Excited Wave ◽  
Highly Sensitive ◽  
Contrast Mechanisms ◽  
Step Thickness ◽  
Thickness Variations

Contrast mechanisms, which are responsible of the various types of image formation, are generally thickness dependant. In the following, two imaging modes in the 100 kV CTEM are described : they are highly sensitive to thickness variations and can be used for quantitative estimations of step heights.Detailed calculations (1) of the bright-field intensity have been carried out in the 3 (or 2N+l)-beam symmetric case. They show that in given conditions, the two important symmetric Bloch waves interfere most strongly at a critical thickness for which they have equal emergent amplitudes (the more excited wave at the entrance surface is also the more absorbed). The transmitted intensity I for a Nd2O3 specimen has been calculated as a function of thickness t. The capacity of the method to detect a step and measure its height can be more clearly deduced from a plot of dl/Idt as shown in fig. 1.

Estimation of the noise in TEM image recorded on “imaging plate”

1987 ◽  
Vol 45 ◽  
pp. 748-749
Author(s):  
T. Oikawa ◽  
N. Mori ◽  
T. Katoh ◽  
Y. Harada ◽  
J. Miyahara ◽  
...  
Keyword(s):  
Low Dose ◽  
Quantum Noise ◽  
Laser Light ◽  
Imaging Plate ◽  
Total System ◽  
Electron Dose ◽  
X Ray ◽  
Image Recording ◽  
Recording Material ◽  
Highly Sensitive

The “Imaging Plate”(IP) is a highly sensitive image recording plate for X-ray radiography. It has been ascertained that the IP has superior properties and high practicability as an image recording material in a TEM. The sensitivity, one of the properties, is about 3 orders higher than that of conventional photo film. The IP is expected to be applied to low dose techniques. In this paper, an estimation of the quantum noise on the TEM image which appears in case of low electron dose on the IP is reported.In this experiment, the JEM-2000FX TEM and an IP having the same size as photo film were used.Figure 1 shows the schematic diagram of the total system including the TEM used in this experiment. In the reader, He-Ne laser light is scanned across the IP, then blue light is emitted from the IP.

High-sensitivity detection of gold labels by high-angle dark-field STEM imaging

1990 ◽  
Vol 48 (3) ◽  
pp. 892-893 ◽  
Author(s):  
Max T. Otten
Keyword(s):  
High Sensitivity ◽  
Dark Field ◽  
Bright Field ◽  
Backscattered Electron Imaging ◽  
Backscattered Electrons ◽  
Average Atomic Number ◽  
Highly Sensitive ◽  
Backscattered Electron ◽  
Electron Imaging ◽  
High Sensitivity Detection

Labelling of antibodies with small gold probes is a highly sensitive technique for detecting specific molecules in biological tissue. Larger gold probes are usually well visible in TEM or STEM Bright-Field images of unstained specimens. In stained specimens, however, the contrast of the stain is frequently the same as that of the gold labels, making it virtually impossible to identify the labels, especially when smaller gold labels are used to increase the sensitivity of the immunolabelling technique. TEM or STEM Dark-Field images fare no better (Figs. 1a and 2a), again because of the absence of a clear contrast difference between gold labels and stain.Potentially much more useful is backscattered-electron imaging, since this will show differences in average atomic number which are sufficiently large between the metallic gold and the stains normally used. However, for the thin specimens and at high accelerating voltages of the STEM, the yield of backscattered electrons is very small, resulting in a very weak signal. Consequently, the backscattered-electron signal is often too noisy for detecting small labels, even for large spot sizes.

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