scholarly journals STRONG DENSITY OF DEFINABLE TYPES AND CLOSED ORDERED DIFFERENTIAL FIELDS

2019 ◽  
Vol 84 (3) ◽  
pp. 1099-1117 ◽  
Author(s):  
QUENTIN BROUETTE ◽  
PABLO CUBIDES KOVACSICS ◽  
FRANÇOISE POINT
Keyword(s):  
Strong Form ◽  
Dimension Function ◽  
Definable Set ◽  
Definable Type ◽  
Differential Fields

AbstractThe following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable set X ⊆ Mn, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields (CODF) are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

Preliminaries

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Valued Fields ◽  
Definable Set ◽  
Valued Field ◽  
Galois Coverings ◽  
Definable Type ◽  
Definable Sets ◽  
Background Material

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

Topological differential fields and dimension functions

2012 ◽  
Vol 77 (4) ◽  
pp. 1147-1164 ◽  
Author(s):  
Nicolas Guzy ◽  
Françoise Point
Keyword(s):  
Dimension Function ◽  
Dimension Functions ◽  
Differential Fields

AbstractWe construct a fibered dimension function in some topological differential fields.

scholarly journals Cell decomposition and dimension function in the theory of closed ordered differential fields

2009 ◽  
Vol 159 (1-2) ◽  
pp. 111-128 ◽  
Author(s):  
Thomas Brihaye ◽  
Christian Michaux ◽  
Cédric Rivière
Keyword(s):  
Cell Decomposition ◽  
Dimension Function ◽  
Differential Fields

Approximate Euler characteristic, dimension, and weak pigeonhole principles

2004 ◽  
Vol 69 (1) ◽  
pp. 201-214
Author(s):  
Jan Krajíček
Keyword(s):  
Euler Characteristic ◽  
Characteristic Dimension ◽  
Order Structure ◽  
Dimension Function ◽  
Pigeonhole Principle ◽  
First Order ◽  
Definable Set ◽  
Definable Sets

AbstractWe define the notion of approximate Euler characteristic of definable sets of a first order structure. We show that a structure admits a non-trivial approximate Euler characteristic if it satisfies weak pigeonhole principle : two disjoint copies of a non-empty definable set A cannot be definably embedded into A, and principle CC of comparing cardinalities: for any two definable sets A, B either A definably embeds in B or vice versa. Also, a structure admitting a non-trivial approximate Euler characteristic must satisfy .Further we show that a structure admits a non-trivial dimension function on definable sets if and only if it satisfies weak pigeonhole principle : for no definable set A with more than one element can A2 definably embed into A.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

Saussurelaisen kielikäsityksen kritiikki

Virittäjä ◽  
2020 ◽  
Vol 124 (1) ◽  
Author(s):  
Mikko Laasanen
Keyword(s):  
Communication System ◽  
Written Language ◽  
Strong Form ◽  
Continuous Speech ◽  
Language Bias ◽  
Context Free ◽  
Ontological Concept

Artikkeli käsittelee saussurelaista kielikäsitystä kohtaan esitettyä kritiikkiä. Artikkelin tavoitteena on puolustaa saussurelaista kielikäsitystä ja esittää Saussure moni-puolisempana ajattelijana kuin mitä Kurssin vahvasti strukturalisesta luennasta voisi päätellä. Artikkelissa tarkastellaan käsitystä kielestä järjestelmänä (Saussuren langue), kontekstivapaata merkitystä, kirjoitetun kielen vääristymää (written language bias), Roy Harrisin kielimyyttiä sekä kielen dynaamisuutta. Artikkelissa esitetään, että langue on sekä metodologinen että ontologinen käsite, joka viittaa sekä kielen järjestäytymättömiin sääntöihin että kielitieteilijän niistä luomaan järjestelmään. Kontekstivapaan merkityksen osalta korostetaan sitä, että jonkinlainen merkityksen pysyvyys on välttämätön osa kieltä kommunikaatiojärjestelmänä. Artikkelissa argumentoidaan kirjoitetun kielen vääristymän vahvaa muotoa vastaan, jonka mukaan esimerkiksi puheen analysoiminen diskreeteiksi yksiköiksi johtuu kirjoitetun kielen vaikutuksesta. Harrisin kielimyytin osalta esitetään, että kyse ei ole Saussuren näkemyksistä vaan Harrisin tulkinnoista. Artikkelissa esitetään myös, että dynaamisuus ei ole yhteensopimaton käsite saussurelaisen kielikäsityksen kanssa.   On the critique of the Saussurean concept of language: some perspectives and counter-arguments The article deals with the critique of the Saussurean concept of language. The purpose of the article is to defend the Saussurean concept of language and to present Saussure as a more versatile thinker than may be assumed from a purely structuralist reading of Course. The article discusses the concept of language as a system (Saussure’s langue), the notion of context-free meaning, the so-called written-language bias, Roy Harris’ language myth, and the notion of dynamicity in language in relation to the Saussurean concept of language. The article begins by arguing that langue is both a methodological and an ontological concept that refers both to the unorganised rules of language and to the system of language rules as organised by the linguist. Second, the author asserts that some kind of permanence of meaning is essential to the concept of language as a communication system. Third, an argument is presented against the strong form of written-language bias, according to which, for instance, the analysis and reduction of continuous speech into discrete units is based on the model of written language. Fourth, the author posits that the language myth, developed by Harris, is not based on Saussure’s views but on Harris’ interpretation of Saussure’s views. The article ends with the contention that the notion of dynamicity is not incompatible with the Saussurean concept of language.

scholarly journals R-continuous functions

1992 ◽  
Vol 15 (1) ◽  
pp. 57-64 ◽  
Author(s):  
Ch. Konstadilaki-Savvapoulou ◽  
D. Janković
Keyword(s):  
Continuous Functions ◽  
Strong Form ◽  
Topological Spaces ◽  
Strong Continuity ◽  
Closed Graph ◽  
Continuity Properties

A strong form of continuity of functions between topological spaces is introduced and studied. It is shown that in many known results, especially closed graph theorems, functions under consideration areR-continuous. Several results in the literature concerning strong continuity properties are generalized and/or improved.

Positive and Negative Constitutionalism and the Limits of Universalism: A Review Essay†

2021 ◽  
Author(s):  
Adrienne Stone ◽  
Lael K Weis
Keyword(s):  
Review Essay ◽  
Weak Form ◽  
Well Being ◽  
Strong Form ◽  
Constitutional Theory ◽  
Full Potential ◽  
Essential Function

Abstract In The Principles of Constitutionalism, Nicholas Barber provides a sophisticated yet highly readable introduction to fundamental constitutional principles. At the same time, Barber seeks to reorient constitutional theory scholarship away from a mistaken ‘negative’ understanding of constitutionalism towards a ‘positive’ understanding. This essay examines that argument. We suggest that the idea of ‘positive constitutionalism’ has a weaker and a stronger sense. In its weak form, the argument calls for greater attention to what constitutions enable as well as what they restrict, and thus serves as a welcome reminder of the full potential of constitutional principles. However, it cannot be regarded as the correction of a widespread mistake. In its strong form, the argument calls for greater recognition that the state’s essential function lies in advancing the ‘well-being’ of its members. Although this amounts to a significant reorientation, it weakens the theory’s claim to universalism. These tensions indicate limitations to efforts to construct general theories of constitutionalism.

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