A Symmetric β-Model
نویسنده
چکیده
Our context is the study of ω-models of subsystems of second order arithmetic [5, Chapter VIII]. As in [5, Chapter VII], a β-model is an ω-model M such that, for all Σ1 sentences φ with parameters from M , φ is true if and only if M |= φ. Theorems 1.1 and 1.3 below are an interesting supplement to the results on β-models which have been presented in Simpson [5, §§VII.2 and VIII.6]. Let HYP denote the set of hyperarithmetical reals. It is well known that, for any β-model M , HYP is properly included in M , and each X ∈ HYP is definable in M .
منابع مشابه
Numerical Determination of Delamination Onset in Laminated Symmetric DCB Specimen
In this study, a novel numerical method is proposed for determination of mode-I interlaminar fracture toughness, GIc, in multi-directional (MD) double cantilever beam (DCB) specimens using fracture properties of unidirectional DCB specimens. Two factors, β and Dc are defined to minimize the undesirable effects on strain energy release rate. β describes the difference between maximum and average...
متن کاملCoefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials
In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.
متن کاملMHD Flow of Blood through Radially Non-symmetric Stenosed Artery: a Hershcel-Bulkley Model (RESEARCH NOTE)
The purpose of this study is to develop a mathematical model for studying the magnetic field effect on blood flow through an axially non-symmetric but radially symmetric atherosclerotic artery. Herschel-Bulkley equation has been taken to represent the non-Newtonian character of blood. The response of magnetic field, stenosis height, shape parameter on velocity, volumetric flow rate in stenotic ...
متن کاملA Finite Element Model for Simulating Flow around a Well with Helically Symmetric Perforations
In a perforated well, fluids enter the wellbore through array of perforation tunnels. These perforations are typically distributed in a helical pattern around the wellbore. Available numerical models to simulate production flow into cased-and-perforated vertical wells have complicated boundary conditions or suffer from high computational costs. This paper presents a simple and at the same time ...
متن کاملBuckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams
The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...
متن کاملDuality in Random Matrix Ensembles for All Β
Gaussian and Chiral β-Ensembles, which generalise well known orthogonal (β = 1), unitary (β = 2), and symplectic (β = 4) ensembles of random Hermitian matrices, are considered. Averages are shown to satisfy duality relations like {β,N, n} ⇔ {4/β, n,N} for all β > 0, where N and n respectively denote the number of eigenvalues and products of characteristic polynomials. At the edge of the spectru...
متن کامل