scholarly journals RELATIVELY EXCHANGEABLE STRUCTURES

2018 ◽  
Vol 83 (2) ◽  
pp. 416-442 ◽  
Author(s):  
HARRY CRANE ◽  
HENRY TOWSNER
Keyword(s):  
Amalgamation Property ◽  
Reference Structure ◽  
Precise Description ◽  
Type Representation ◽  
Relational Structures ◽  
Random Structures ◽  
Image Position

AbstractWe study random relational structures that are relatively exchangeable—that is, whose distributions are invariant under the automorphisms of a reference structure ${M}$. When ${M}$ is ultrahomogeneous and has trivial definable closure, all random structures relatively exchangeable with respect to $m$ satisfy a general Aldous–Hoover-type representation. If ${M}$ also satisfies the n-disjoint amalgamation property (n-DAP) for all $n \ge 1$, then relatively exchangeable structures have a more precise description whereby each component depends locally on ${M}$.

Zero-one laws with variable probability

1993 ◽  
Vol 58 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Joel Spencer
Keyword(s):  
Probability Space ◽  
Equal Weight ◽  
Order Property ◽  
First Order ◽  
Random Structures ◽  
Monadic Logic ◽  
Edge Probability ◽  
Image Position ◽  
Labelled Graphs ◽  
Variable Probability

One of this author's favorite theorems has long been the Zero-One law discovered independently by Glebskii et al. [12] and Ron Fagin [10]. Let A be any first-order property of graphs and let µn(A) be the proportion of labelled graphs on n vertices for which A holds. ThenThis result has inspired much work by logicians, generally in the direction of showing (1) for some powerful languages. Thus it is known [5] that (1) holds when A is a sentence in fixed point logic and it is known [13] that (1) does not always hold when A is a sentence in second-order monadic logic. Here, however, we explore recent work in a totally different direction. Let G(n, p) denote the random graph on n vertices with edge probability p. (In §2 we define the random structures we will deal with.) A property A is an event in the probability space and Pr[G(n, p) ╞ A] is well defined. When p = 1/2, each labelled graph on n vertices has equal weight so that (1) may be rewrittenFagin's proof actually gives that (2) holds for any constant 0 < p < 1.

scholarly journals AMALGAMABLE DIAGRAM SHAPES

2019 ◽  
Vol 84 (1) ◽  
pp. 88-101
Author(s):  
RUIYUAN CHEN
Keyword(s):  
Closed Subset ◽  
Amalgamation Property ◽  
Finitely Generated ◽  
Finite Poset ◽  
Simple Rules ◽  
Joint Embedding ◽  
Image Position ◽  
Joint Embedding Property ◽  
Simply Connected

AbstractA category has the amalgamation property (AP) if every pushout diagram has a cocone, and the joint embedding property (JEP) if every finite coproduct diagram has a cocone. We show that for a finitely generated category I, the following are equivalent: (i) every I-shaped diagram in a category with the AP and the JEP has a cocone; (ii) every I-shaped diagram in the category of sets and injections has a cocone; (iii) a certain canonically defined category ${\cal L}\left( {\bf{I}} \right)$ of “paths” in I has only idempotent endomorphisms. When I is a finite poset, these are further equivalent to: (iv) every upward-closed subset of I is simply-connected; (v) I can be built inductively via some simple rules. Our proof also shows that these conditions are decidable for finite I.

scholarly journals WEAK SATURATION AND WEAK AMALGAMATION PROPERTY

2019 ◽  
Vol 84 (3) ◽  
pp. 929-936
Author(s):  
IVAN DI LIBERTI
Keyword(s):  
Model Theory ◽  
Existence And Uniqueness ◽  
Classical Model ◽  
Sufficient Conditions ◽  
Amalgamation Property ◽  
Accessible Categories ◽  
Image Position ◽  
Accessible Category ◽  
Weak Amalgamation

AbstractWe study the two model-theoretic concepts of weak saturation and weak amalgamation property in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly saturated objects of an accessible category ${\cal K}$. We discuss the implications of this fact in classical model theory.

On generic structures with a strong amalgamation property

2009 ◽  
Vol 74 (3) ◽  
pp. 721-733 ◽  
Author(s):  
Koichiro Ikeda ◽  
Hirotaka Kikyo ◽  
Akito Tsuboi
Keyword(s):  
Amalgamation Property ◽  
Generic Model ◽  
Dimension Function ◽  
Finite Structures ◽  
Image Position ◽  
Generic Structures

AbstractLet be a finite relational language and α = (αR: R ∈ ) a tuple with 0 < αR ≤ 1 for each R ∈ . Consider a dimension functionwhere each eR(A) is the number of realizations of R in A. Let Kα be the class of finite structures A such that δα (X) ≥ 0 for any substructure X of A. We show that the theory of the generic model of Kα is AE-axiomatizable for any α.

ON ${\omega _1}$-STRONGLY COMPACT CARDINALS

2014 ◽  
Vol 79 (01) ◽  
pp. 266-278 ◽  
Author(s):  
JOAN BAGARIA ◽  
MENACHEM MAGIDOR
Keyword(s):  
Measurable Cardinal ◽  
Second Order ◽  
Singular Cardinal ◽  
Strongly Compact Cardinal ◽  
Compact Cardinal ◽  
Relational Structures ◽  
Uncountable Cardinal ◽  
Image Position ◽  
Strongly Compact Cardinals ◽  
Order Reflection

Abstract An uncountable cardinal κ is called ${\omega _1}$ -strongly compact if every κ-complete ultrafilter on any set I can be extended to an ${\omega _1}$ -complete ultrafilter on I. We show that the first ${\omega _1}$ -strongly compact cardinal, ${\kappa _0}$ , cannot be a successor cardinal, and that its cofinality is at least the first measurable cardinal. We prove that the Singular Cardinal Hypothesis holds above ${\kappa _0}$ . We show that the product of Lindelöf spaces is κ-Lindelöf if and only if $\kappa \ge {\kappa _0}$ . Finally, we characterize ${\kappa _0}$ in terms of second order reflection for relational structures and we give some applications. For instance, we show that every first-countable nonmetrizable space has a nonmetrizable subspace of size less than ${\kappa _0}$ .

Simple Identification of Electron Diffraction Ring Patterns

1969 ◽  
Vol 27 ◽  
pp. 160-161
Author(s):  
Carolyn Nohr ◽  
Ann Ayres
Keyword(s):  
Electron Microscope ◽  
Electron Diffraction ◽  
Diffraction Ring ◽  
Image Position

Texts on electron diffraction recommend that the camera constant of the electron microscope be determine d by calibration with a standard crystalline specimen, using the equation

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

A Magnetic Spectrometer for a Scanning Transmission Electron Microscope

1974 ◽  
Vol 32 ◽  
pp. 436-437
Author(s):  
A. Kosiara ◽  
J. W. Wiggins ◽  
M. Beer
Keyword(s):  
Scanning Transmission Electron Microscope ◽  
Magnetic Spectrometer ◽  
Fringe Field ◽  
Curvature Radius ◽  
Magnetic Pole ◽  
Quadrupole Field ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
Under Construction ◽  
Image Position

A magnetic spectrometer to be attached to the Johns Hopkins S. T. E. M. is under construction. Its main purpose will be to investigate electron interactions with biological molecules in the energy range of 40 KeV to 100 KeV. The spectrometer is of the type described by Kerwin and by Crewe Its magnetic pole boundary is given by the equationwhere R is the electron curvature radius. In our case, R = 15 cm. The electron beam will be deflected by an angle of 90°. The distance between the electron source and the pole boundary will be 30 cm. A linear fringe field will be generated by a quadrupole field arrangement. This is accomplished by a grounded mirror plate and a 45° taper of the magnetic pole.

Optimizing conditions for x-ray microchemical analysis in analytical electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 548-549 ◽  
Author(s):  
N. J. Zaluzec
Keyword(s):  
Solid Angle ◽  
Analytical Electron Microscopy ◽  
Incident Beam ◽  
Thin Foil ◽  
Experimental Conditions ◽  
X Ray ◽  
Microchemical Analysis ◽  
Analytical Electron ◽  
Image Position ◽  
Incident Beam Energy

The ultimate sensitivity of microchemical analysis using x-ray emission rests in selecting those experimental conditions which will maximize the measured peak-to-background (P/B) ratio. This paper presents the results of calculations aimed at determining the influence of incident beam energy, detector/specimen geometry and specimen composition on the P/B ratio for ideally thin samples (i.e., the effects of scattering and absorption are considered negligible). As such it is assumed that the complications resulting from system peaks, bremsstrahlung fluorescence, electron tails and specimen contamination have been eliminated and that one needs only to consider the physics of the generation/emission process.The number of characteristic x-ray photons (Ip) emitted from a thin foil of thickness dt into the solid angle dΩ is given by the well-known equation

X-ray microanalysis of thin specimens in the transmission electron microscope at voltages up to 1000 Kv.

1978 ◽  
Vol 36 (1) ◽  
pp. 540-541
Author(s):  
G. Cliff ◽  
M.J. Nasir ◽  
G.W. Lorimer ◽  
N. Ridley
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Weight Fraction ◽  
Present Series ◽  
Constant Independent ◽  
X Ray ◽  
Transmission Electron ◽  
Series Of Experiments ◽  
Image Position ◽  
X Ray Absorption

In a specimen which is transmission thin to 100 kV electrons - a sample in which X-ray absorption is so insignificant that it can be neglected and where fluorescence effects can generally be ignored (1,2) - a ratio of characteristic X-ray intensities, I1/I2 can be converted into a weight fraction ratio, C1/C2, using the equationwhere k12 is, at a given voltage, a constant independent of composition or thickness, k12 values can be determined experimentally from thin standards (3) or calculated (4,6). Both experimental and calculated k12 values have been obtained for K(11<Z>19),kα(Z>19) and some Lα radiation (3,6) at 100 kV. The object of the present series of experiments was to experimentally determine k12 values at voltages between 200 and 1000 kV and to compare these with calculated values.The experiments were carried out on an AEI-EM7 HVEM fitted with an energy dispersive X-ray detector.

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