TY - JOUR
AU - Basheyeva, A. O.
PY - 2018/08/22
Y2 - 2024/10/05
TI - w-independent quasi-equational basis of differential groupoids
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 95
IS - 3
SE - Mathematics
DO - 10.26577/jmmcs-2017-3-465
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/465
SP - 21-31
AB - <p>The search for the solutions of the finite basis problem was and still is under the influence of<br>the problem of Alfred Tarski (Tarski, 1966: 275–288), who asked in 1966: if there is exists an<br>algorithm for deciding whether the quasi-equational theory of a finite set of finite algebras which<br>is assumed additionally to be equational, is finitely based. Tarski’s problem has been solved in<br>the negative by Ralph McKenzie (McKenzie, 1996: 49–104). The negative solution of Tarski’s<br>problem actually makes the finite basis problem more interesting and worthy of continued effort.<br>If Tarski’s problem had had a positive solution, the status of the finite basis problem would be<br>totally different. It would probably still exist, however, the main stream of the scientific effort would<br>go toward improving the known algorithms and classifying their complexity. However, the main<br>stream of the scientific effort would go toward improving the known algorithms and classifying<br>their complexity. We want to stress that the analogue of Tarski’s problem for the quasi-equational<br>theories that are not equational is unsolved. There is, however, a common believe that it will<br>also have a negative answer. It has been established at the end of the 1990-ties by a number of<br>researchers marvelous proof for the negative solution of Tarski’s problem cannot be easily modified<br>for quasi-equational theories. So today independent bases of quasiidentities have been found for<br>many classes of algebras and models. We will note that recently in work (Kravchenko, 2017с) has<br>found the general and sufficient condition for existence of a continuum of quasivarieties without<br>independent basis of quasiidentities, but with w - independent bases of quasiidentities. However<br>differential gruppoids aren’t sutisfied to these conditions and in this work we continued to study<br>the an independent quasiaquational basis of quasivarieties of differential gruppoids. The main<br>result is exists a continuum of quasivarieties of differential gruppoid which have w - independent<br>basis of quasiidentities.</p>
ER -