Complete Theories

1957 ◽  
Vol 41 (338) ◽  
pp. 303
Author(s):  
R. L. Goodstein ◽  
Abraham Robinson
Keyword(s):  
Complete Theories

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.

Complete Theories

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

The Logic of Violence

Politics ◽  
2002 ◽  
Vol 22 (2) ◽  
pp. 109-117 ◽  
Author(s):  
Diego Muro-Ruiz
Keyword(s):  
General Theory ◽  
Political Science ◽  
Violent Behaviour ◽  
Causes Of Violence ◽  
Complete Theories ◽  
The Individual

To date, there is no synthetic, general theory of violence able to integrate the less complete theories of violent behaviour. There is little agreement among researchers about the causes of violence (not to mention what to do about it) and the field has become vast in terms of literature. This paper reviews theories of violence, mostly from sociology, political science and psychology both at the level of the individual and the collective. The paper is divided in two parts: the first deals with theories that see violence as a reaction, the second deals with those theories that see violence as a mean to attain goals.

GANZSTELLENSÄTZE IN THEORIES OF VALUED FIELDS

2008 ◽  
Vol 08 (01) ◽  
pp. 1-22 ◽  
Author(s):  
DEIRDRE HASKELL ◽  
YOAV YAFFE
Keyword(s):  
Valuation Ring ◽  
Uniform Method ◽  
Algebraic Characterization ◽  
Valued Fields ◽  
Definable Set ◽  
Valued Field ◽  
Complete Theories ◽  
The Given ◽  
Relevant Class

The purpose of this paper is to study an analogue of Hilbert's seventeenth problem for functions over a valued field which are integral definite on some definable set; that is, that map the given set into the valuation ring. We use model theory to exhibit a uniform method, on various theories of valued fields, for deriving an algebraic characterization of such functions. As part of this method we refine the concept of a function being integral at a point, and make it dependent on the relevant class of valued fields. We apply our framework to algebraically closed valued fields, model complete theories of difference and differential valued fields, and real closed valued fields.

A remark concerning decidability of complete theories

1950 ◽  
Vol 15 (4) ◽  
pp. 277-279 ◽  
Author(s):  
Antoni Janiczak
Keyword(s):  
Finite Number ◽  
Decision Procedure ◽  
Effective Procedure ◽  
Undecidable Theory ◽  
Consistent Extension ◽  
Complete Theories ◽  
General Conditions

A formalized theory is called complete if for each sentence expressible in this theory either the sentence itself or its negation is provable.A theory is called deciddble if there exists an effective procedure (called decision-procedure) which enables one to decide of each sentence, in a finite number of steps, whether or not it is provable in the theory.It is known that there exist complete but undecidable theories. There exist, namely, the so called essentially undecidable theories, i.e. theories which are undecidable and remain so after an arbitrary consistent extension of the set of axioms. Using the well-known method of Lindenbaum we can therefore obtain from each such theory a complete and undecidable theory.The aim of this paper is to prove a theorem which shows that complete theories satisfying certain very general conditions are always decidable. In somewhat loose formulation these conditions are: There exist four effective methods M1, M2, M3, M4, such that(a) M1 enables us to decide in each case whether or not any given formula is a sentence of the theory;(b) M2 gives an enumeration of all axioms of the theory;(c) the rules of inference can be arranged in a sequence R1, R2, … such that if p1, … pk, r are arbitrary sentences of the theory, we can decide by M3 whether or not r results from p1, … pk, by the n-th rule;(d) M4 enables us to construct effectively the negation of each effectively given sentence.In order to express these conditions more precisely we shall make use of an arithmetization of the considered theory .

Relatively Complete Theories

1976 ◽  
Vol 22 (1) ◽  
pp. 245-250
Author(s):  
D. W. H. Gillam
Keyword(s):  
Complete Theories

E-scaping the ageing body? Computer technologies and embodiment in later life

2010 ◽  
Vol 30 (6) ◽  
pp. 987-1009 ◽  
Author(s):  
CHRISTINA E. BUSE
Keyword(s):  
Technology Use ◽  
Internet Use ◽  
Practical Knowledge ◽  
Qualitative Interviews ◽  
Later Life ◽  
The Body ◽  
Computer Technologies ◽  
Computing Skills ◽  
Ageing Body ◽  
Complete Theories

ABSTRACTThis paper explores the embodied dimensions of computer and internet use in later life, and examines how technology use relates to constructions and experiences of the ageing body. It is argued that previous research on technology use and embodiment has neglected older bodies, in contrast to research on gender and disability. Furthermore, while earlier theorisations presented internet use as disembodied, it is argued that the experience of using such technologies is grounded in our embodiment. In the light of these limitations and arguments for more complete theories of the body, this paper explores how technology use relates to various aspects of embodiment. These issues are examined in the light of data from qualitative interviews and time-use diaries completed by retirees in 17 households in the United Kingdom. By examining the ‘technobiographies’ of these older computer users, it is shown that changes in body techniques are prompted and in some cases required by broader cultural and technological change. The findings evince the process of acquiring computing skills as an embodied competency, and as a form of ‘practical knowledge’ that can only be ‘learned by doing’. These experiences of technology use were embedded within constructions and experiences of ageing bodies. Although the participants drew on discourses of ageing in complex ways, their coding of computer technologies in terms of the competences of youth often reproduced hierarchies between young and old bodies.

Direct product decomposition of theories of modules

1979 ◽  
Vol 44 (1) ◽  
pp. 77-88 ◽  
Author(s):  
Steven Garavaglia
Keyword(s):  
Direct Product ◽  
Regular Ring ◽  
Decomposition Theorem ◽  
Direct Products ◽  
Product Decomposition ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Direct Product Decomposition ◽  
Von Neumann Regular ◽  
Complete Theories

This paper is mainly concerned with describing complete theories of modules by decomposing them (up to elementary equivalence) into direct products of simpler modules. In §1, I give a decomposition theorem which works for arbitrary direct product theories T. Given such a T, I define T-indecomposable structures and show that every model of T is elementarily equivalent to a direct product of T-indecomposable models of T. In §2, I show that if R is a commutative ring then every R-module is elementarily equivalent to ΠMM where M ranges over the maximal ideals of R and M is the localization of at M. This is applied to prove that if R is a commutative von Neumann regular ring and TR is the theory of R-modules then the TR-indecomposables are precisely the cyclic modules of the form R/M where M is a maximal ideal. In §3, I use the decomposition established in §2 to characterize the ω1-categorical and ω-stable modules over a countable commutative von Neumann regular ring and the superstable modules over a commutative von Neumann regular ring of arbitrary cardinality. In the process, I also prove several general characterizations of ω-stable and superstable modules; e.g., if R is any countable ring, then an R-moduIe is ω-stable if and only if every R-module elementarily equivalent to it is equationally compact.

Theories with finitely many models

1986 ◽  
Vol 51 (2) ◽  
pp. 374-376 ◽  
Author(s):  
Simon Thomas
Keyword(s):  
Natural Number ◽  
Complete Theory ◽  
Elementary Equivalence ◽  
First Order ◽  
Finite Models ◽  
Simple Observation ◽  
Finite Structure ◽  
Order Language ◽  
Complete Theories

If L is a first order language and n is a natural number, then Ln is the set of formulas which only make use of the variables x1,…,xn. While every finite structure is determined up to isomorphism by its theory in L, the same is no longer true in Ln. This simple observation is the source of a number of intriguing questions. For example, Poizat [2] has asked whether a complete theory in Ln which has at least two nonisomorphic finite models must necessarily also have an infinite one. The purpose of this paper is to present some counterexamples to this conjecture.Theorem. For each n ≤ 3 there are complete theories in L2n−2andL2n−1having exactly n + 1 models.In our notation and definitions, we follow Poizat [2]. To test structures for elementary equivalence in Ln, we shall use the modified Ehrenfeucht-Fraïssé games of Immerman [1]. For convenience, we repeat his definition here.Suppose that L is a purely relational language, each of the relations having arity at most n. Let and ℬ be two structures for L. Define the Ln game on and ℬ as follows. There are two players, I and II, and there are n pairs of counters a1, b1, …, an, bn. On each move, player I picks up any of the counters and places it on an element of the appropriate structure.

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