Logical quantizations of first-order structures

1996 ◽  
Vol 35 (3) ◽  
pp. 495-517 ◽  
Author(s):  
Hirokazu Nishimura
Keyword(s):  
First Order ◽  
Order Structures

TYPE-DEFINABILITY, COMPACT LIE GROUPS, AND o-MINIMALITY

2004 ◽  
Vol 04 (02) ◽  
pp. 147-162 ◽  
Author(s):  
ANAND PILLAY
Keyword(s):  
Compact Lie Group ◽  
Compact Lie Groups ◽  
First Order ◽  
Special Cases ◽  
Definable Groups ◽  
Small Index ◽  
Logic Topology ◽  
The Right ◽  
Study Type ◽  
Order Structures

We study type-definable subgroups of small index in definable groups, and the structure on the quotient, in first order structures. We raise some conjectures in the case where the ambient structure is o-minimal. The gist is that in this o-minimal case, any definable group G should have a smallest type-definable subgroup of bounded index, and that the quotient, when equipped with the logic topology, should be a compact Lie group of the "right" dimension. I give positive answers to the conjectures in the special cases when G is 1-dimensional, and when G is definably simple.

scholarly journals On minimal ordered structures

2005 ◽  
Vol 78 (92) ◽  
pp. 65-72 ◽  
Author(s):  
Predrag Tanovic
Keyword(s):  
Strong Form ◽  
Order Property ◽  
Ordered Structures ◽  
First Order ◽  
Order Structures

We partially describe minimal, first-order structures which have a strong form of the strict order property.

Compactly Representing First-Order Structures for Static Analysis

2002 ◽  
pp. 196-212 ◽  
Author(s):  
R. Manevich ◽  
G. Ramalingam ◽  
J. Field ◽  
D. Goyal ◽  
M. Sagiv
Keyword(s):  
Static Analysis ◽  
First Order ◽  
Order Structures

scholarly journals A notion of functional completeness for first-order structure

2005 ◽  
Vol 2005 (14) ◽  
pp. 2207-2215
Author(s):  
Etienne R. Alomo Temgoua ◽  
Marcel Tonga
Keyword(s):  
Order Structure ◽  
Functional Completeness ◽  
First Order ◽  
Term Functions ◽  
Order Structures

Using☆-congruences and implications, Weaver (1993) introduced the concepts of prevariety and quasivariety of first-order structures as generalizations of the corresponding concepts for algebras. The notion of functional completeness on algebras has been defined and characterized by Burris and Sankappanavar (1981), Kaarli and Pixley (2001), Pixley (1996), and Quackenbush (1981). We study the notion of functional completeness with respect to☆-congruences. We extend some results on functionally complete algebras to first-order structuresA=(A;FA;RA)and find conditions for these structures to have a compatible Pixley function which is interpolated by term functions on suitable subsets of the base setA.

scholarly journals Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic

2019 ◽  
Vol 23 (7) ◽  
pp. 2177-2186 ◽  
Author(s):  
Guillermo Badia ◽  
Vicent Costa ◽  
Pilar Dellunde ◽  
Carles Noguera
Keyword(s):  
Fuzzy Logic ◽  
First Order ◽  
Mathematical Fuzzy Logic ◽  
Order Structures

scholarly journals A Reiterman theorem for pseudovarieties of finite first-order structures

1996 ◽  
Vol 35 (4) ◽  
pp. 577-595 ◽  
Author(s):  
J. -E. Pin ◽  
P. Weil
Keyword(s):  
First Order ◽  
Order Structures

The first-order structure of weakly Dedekind-finite set

2005 ◽  
Vol 70 (4) ◽  
pp. 1161-1170 ◽  
Author(s):  
A. C. Walczak-Typke
Keyword(s):  
Order Structure ◽  
Finite Sets ◽  
First Order ◽  
Finite Set ◽  
Infinite Sets ◽  
Order Structures

AbstractWe show that infinite sets whose power-sets are Dedekind-finite can only carry ℵ0-categorical first order structures. We identify other subclasses of this class of Dedekind-finite sets, and discuss their possible first order structures.

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