On the undecidability of elementary theories of certain fields

1965 ◽  
pp. 36-44 ◽  
Author(s):  
A. I. Mal′cev
Keyword(s):  
Elementary Theories

Applications of Finite Models Properties in Approximation and Algorithmic Logics

1991 ◽  
Vol 14 (1) ◽  
pp. 91-108
Author(s):  
Jarosław Stepaniuk
Keyword(s):  
Finite Models ◽  
Elementary Theories

The purpose of this paper is to investigate some aspects concerning elementary theories of finite models and to give the applications in approximation logics and algorithmic theory of dictionaries.

Formularity of sets of Mal'tsev bases, and elementary theories of finite algebras. I

1983 ◽  
Vol 23 (5) ◽  
pp. 711-724
Author(s):  
A. G. Myasnikov ◽  
V. N. Remeslennikov
Keyword(s):  
Finite Algebras ◽  
Elementary Theories

Linear $ \mathrm{GLP}$-algebras and their elementary theories

2016 ◽  
Vol 80 (6) ◽  
pp. 1159-1199
Author(s):  
F N Pakhomov
Keyword(s):  
Elementary Theories

scholarly journals On Certain Axiomatizations of Arithmetic of Natural and Integer Numbers

Axioms ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 103 ◽  
Author(s):  
Urszula Wybraniec-Skardowska
Keyword(s):  
Natural Number ◽  
Ordered Sets ◽  
Natural Numbers ◽  
Elementary Theories

The systems of arithmetic discussed in this work are non-elementary theories. In this paper, natural numbers are characterized axiomatically in two different ways. We begin by recalling the classical set P of axioms of Peano’s arithmetic of natural numbers proposed in 1889 (including such primitive notions as: set of natural numbers, zero, successor of natural number) and compare it with the set W of axioms of this arithmetic (including the primitive notions like: set of natural numbers and relation of inequality) proposed by Witold Wilkosz, a Polish logician, philosopher and mathematician, in 1932. The axioms W are those of ordered sets without largest element, in which every non-empty set has a least element, and every set bounded from above has a greatest element. We show that P and W are equivalent and also that the systems of arithmetic based on W or on P, are categorical and consistent. There follows a set of intuitive axioms PI of integers arithmetic, modelled on P and proposed by B. Iwanuś, as well as a set of axioms WI of this arithmetic, modelled on the W axioms, PI and WI being also equivalent, categorical and consistent. We also discuss the problem of independence of sets of axioms, which were dealt with earlier.

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