Classification and interpretation

1989 ◽  
Vol 54 (1) ◽  
pp. 138-159 ◽  
Author(s):  
Andreas Baudisch
Keyword(s):  
Order Property ◽  
Similarity Type ◽  
Complete Theories

AbstractLet S and T be countable complete theories. We assume that T is superstable without the dimensional order property, and S is interpretable in T in such a way that every model of S is coded in a model of T. We show that S does not have the dimensional order property, and we discuss the question of whether Depth(S) ≤ Depth(T). For Mekler's uniform interpretation of arbitrary theories S of finite similarity type into suitable theories TS of groups we show that Depth(S) ≤ Depth(TS) ≤ 1 + Depth(S).

On chains of relatively saturated submodels of a model without the order property

1991 ◽  
Vol 56 (1) ◽  
pp. 124-128 ◽  
Author(s):  
Rami Grossberg
Keyword(s):  
Existence Theorems ◽  
Order Property ◽  
Similarity Type

AbstractLet M be a given model with similarity type L = L(M), and let L′ be any fragment of L∣L(M∣+,ω of cardinality ∣L(M)∣. We call N ≺ ML′-relatively saturated iff for every B ⊆ N of cardinality less than ∥N∥ every L′-type over B which is realized in M is realized in N. We discuss the existence of such submodels.The following are corollaries of the existence theorems.(1) If M is of cardinality at least ℶω1, and fails to have the ω order property, then there exists N ≺ M which is relatively saturated in M of cardinality ℶω1.(2) Assume GCH. Let ψ ∈ Lω1, ω, and let L′ ⊆ Lω1, ω be a countable fragment containing ψ. If ∃χ > ℵ0 such that I(χ, ψ) < 2χ, then for every M ⊨ ψ and every cardinal λ < ∥M∥ of uncountable cofinality, M has an L′-relatively saturated submodel of cardinality λ.

On the Probabilistic Nature of Observable Phenomena

2019 ◽  
Author(s):  
Muhammad Ali
Keyword(s):  
Quantum Mechanics ◽  
Complete Theory ◽  
Interpretation Of Quantum Mechanics ◽  
Multiple Realities ◽  
Lack Of Information ◽  
Complete Theories ◽  
Probabilistic Nature

This paper proposes a Gadenkan experiment named “Observer’s Dilemma”, to investigate the probabilistic nature of observable phenomena. It has been reasoned that probabilistic nature in, otherwise uniquely deterministic phenomena can be introduced due to lack of information of underlying governing laws. Through theoretical consequences of the experiment, concepts of ‘Absolute Complete’ and ‘Observably Complete” theories have been introduced. Furthermore, nature of reality being ‘absolute’ and ‘observable’ have been discussed along with the possibility of multiple realities being true for observer. In addition, certain aspects of quantum mechanics have been interpreted. It has been argued that quantum mechanics is an ‘observably complete’ theory and its nature is to give probabilistic predictions. Lastly, it has been argued that “Everettian - Many world” interpretation of quantum mechanics is very real and true in the framework of ‘observable nature of reality’, for humans.

Metaontology

2018 ◽  
Author(s):  
Uriah Kriegel
Keyword(s):  
Second Order ◽  
Order Property ◽  
First Order ◽  
First Approximation

Brentano’s theory of judgment serves as a springboard for his conception of reality, indeed for his ontology. It does so, indirectly, by inspiring a very specific metaontology. To a first approximation, ontology is concerned with what exists, metaontology with what it means to say that something exists. So understood, metaontology has been dominated by three views: (i) existence as a substantive first-order property that some things have and some do not, (ii) existence as a formal first-order property that everything has, and (iii) existence as a second-order property of existents’ distinctive properties. Brentano offers a fourth and completely different approach to existence talk, however, one which falls naturally out of his theory of judgment. The purpose of this chapter is to present and motivate Brentano’s approach.

scholarly journals On the boundary layer arising in the spin-up of a stratified fluid in a container with sloping walls

1997 ◽  
Vol 335 ◽  
pp. 233-259 ◽  
Author(s):  
P. W. DUCK ◽  
M. R. FOSTER ◽  
R. E. HEWITT
Keyword(s):  
Boundary Layer ◽  
Layer Structure ◽  
Outer Region ◽  
Stratified Fluid ◽  
Main Body ◽  
Similarity Type ◽  
Cone Apex ◽  
Uniform Solution ◽  
Steady Solutions ◽  
Finite Time Singularity

In this paper we consider the boundary layer that forms on the sloping walls of a rotating container (notably a conical container), filled with a stratified fluid, when flow conditions are changed abruptly from some initial (uniform) state. The structure of the solution valid away from the cone apex is derived, and it is shown that a similarity-type solution is appropriate. This system, which is inherently nonlinear in nature, is solved numerically for several flow regimes, and the results reveal a number of interesting and diverse features.In one case, a steady state is attained at large times inside the boundary layer. In a second case, a finite-time singularity occurs, which is fully analysed. A third scenario involves a double boundary-layer structure developing at large times, most significantly including an outer region that grows in thickness as the square-root of time.We also consider directly the nonlinear fully steady solutions to the problem, and map out in parameter space the likely ultimate flow behaviour. Intriguingly, we find cases where, when the rotation rate of the container is equal to that of the main body of the fluid, an alternative nonlinear state is preferred, rather than the trivial (uniform) solution.Finally, utilizing Laplace transforms, we re-investigate the linear initial-value problem for small differential spin-up studied by MacCready & Rhines (1991), recovering the growing-layer solution they found. However, in contrast to earlier work, we find a critical value of the buoyancy parameter beyond which the solution grows exponentially in time, consistent with our nonlinear results.

scholarly journals Mal’tsev products of varieties, I

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Tomasz Penza ◽  
Anna B. Romanowska
Keyword(s):  
Sufficient Condition ◽  
Similarity Type

AbstractWe investigate the Mal’tsev product $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W of two varieties $$\mathcal {V}$$ V and $$\mathcal {W}$$ W of the same similarity type. While such a product is usually a quasivariety, it is not necessarily a variety. We give an equational base for the variety generated by $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W in terms of identities satisfied in $$\mathcal {V}$$ V and $$\mathcal {W}$$ W . Then the main result provides a new sufficient condition for $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W to be a variety: If $$\mathcal {W}$$ W is an idempotent variety and there are terms f(x, y) and g(x, y) such that $$\mathcal {W}$$ W satisfies the identity $$f(x,y) = g(x,y)$$ f ( x , y ) = g ( x , y ) and $$\mathcal {V}$$ V satisfies the identities $$f(x,y) = x$$ f ( x , y ) = x and $$g(x,y) = y$$ g ( x , y ) = y , then $$\mathcal {V}\circ \mathcal {W}$$ V ∘ W is a variety. We provide a number of examples and applications of this result.

Weakly atomic-compact relational structures

1971 ◽  
Vol 36 (1) ◽  
pp. 129-140 ◽  
Author(s):  
G. Fuhrken ◽  
W. Taylor
Keyword(s):  
Abelian Group ◽  
Model Theory ◽  
Compact Abelian Group ◽  
Finite Subset ◽  
Relational Structure ◽  
Similarity Type ◽  
First Order ◽  
Relational Structures ◽  
Order Language ◽  
Weakly Atomic

A relational structure is called weakly atomic-compact if and only if every set Σ of atomic formulas (taken from the first-order language of the similarity type of augmented by a possibly uncountable set of additional variables as “unknowns”) is satisfiable in whenever every finite subset of Σ is so satisfiable. This notion (as well as some related ones which will be mentioned in §4) was introduced by J. Mycielski as a generalization to model theory of I. Kaplansky's notion of an algebraically compact Abelian group (cf. [5], [7], [1], [8]).

scholarly journals POSITIVE FRAGMENTS OF RELEVANCE LOGIC AND ALGEBRAS OF BINARY RELATIONS

2010 ◽  
Vol 4 (1) ◽  
pp. 81-105 ◽  
Author(s):  
ROBIN HIRSCH ◽  
SZABOLCS MIKULÁS
Keyword(s):  
Equational Theory ◽  
Relevance Logic ◽  
Binary Relations ◽  
Finitely Based ◽  
Similarity Type ◽  
Relation Composition

We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.

Stability of nilpotent groups of class 2 and prime exponent

1981 ◽  
Vol 46 (4) ◽  
pp. 781-788 ◽  
Author(s):  
Alan H. Mekler
Keyword(s):  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Stability Class ◽  
Similarity Type ◽  
Nilpotent Class ◽  
Prime Exponent

AbstractLet p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M.Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes.Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

Complete Theories

1976 ◽  
pp. 349-364
Author(s):  
J. Donald Monk
Keyword(s):  
Complete Theories
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