| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 48 Number 6
Volume 48 Number 5
Volume 48 Number 4
Volume 48 Number 3
Volume 48 Number 2
Volume 48S Number 1
Earlier issues
Volume 39 Number 2 Volume 39S Number 1 Volume 39 Number 3

previous article next article

Research articles

ScienceAsia 39S (2013): 19-24 |doi: 10.2306/scienceasia1513-1874.2013.39S.019

The structure of lattices of positive existential formulae of (Δ−PJ)-theories

A.R. Yeshkeyev

ABSTRACT:     This article is related to one of the main branches of mathematical logic, model theory, and more precisely to what is called eastern model theory. This part of model theory is concerned with the study of incomplete inductive theories and more precisely Jonsson theories and some of their positive generalizations. It examines the model-theoretical properties of positive Jonsson theories. In particular, the lattice of special formulae is considered. In the study of complete theories one of the main methods is to use the properties of a topological space Sn(T). In the case of positive Jonsson theory, we can consider the lattice En+(T) of existential formulae, which is a sublattice of the Boolean algebra Fn+(T). The main aim of this article is to develop the basic concepts and methods of that part of model theory which will provide an opportunity for fruitful studies of Jonsson theories and some of its positive generalizations. Our technique is standard in the study of incomplete theories. The method consists of the translation of the elementary properties of the centre of a Jonsson theory into the theory itself.

Download PDF

2 Downloads 1169 Views

The Institution of Applied Mathematics, Karaganda State University named after E. A. Buketov, Karaganda, Kazakhstan

* Corresponding author, E-mail: modth1705@mail.ru

Received 7 Jan 2013, Accepted 5 Apr 2013