A question posed by Bergstra and Tiuryn (Q1092893)

\textit{J. Bergstra} and \textit{J. Tiuryn} [Fundam. Inf. 4, 661-674 (1981; Zbl 0487.68017); Fundamentals of computation theory '79, Proc. Conf., Berlin/Wendisch-Rietz 1979, 58-63 (1979; Zbl 0456.68025)] have shown that any algebra without proper subalgebras containing a constant in its signature is uniquely defined up to isomorphism by some family of universal propositions of the logic of effective definitions. In the cited works they also pose the question whether or not this is true of arbitrary algebras without proper subalgebras. In the present work we will use a theoretical model of finite forcing to obtain a negative answer to that question, and we will present an example of an algebra without proper subalgebras which is not defined up to isomorphism by any family consisting of universal and existential propositions of the logic of effective definitions. It has been found, however, that any constructible (in the sense of \textit{A. I. Mal'tsev} [Usp. Mat. Nauk 16, No.3(99), 3-60 (1961; Zbl 0129.259)]) algebra without proper subalgebras is uniquely defined by some set of universal propositions of that logic in the case of all constructible algebras of a given signature. An example is presented of a constructible algebra which has no proper subalgebras and which is not defined in that manner in the class of all algebras.