Ladislav Rieger: Algebraic Methods of Mathematical Logic.

Academia, Prague, 1967, 210 Seiten. Gebunden Leinen.

This monograph appears four years after the author's death in 1963. Ladislav Svante Rieger (b. 1916; for a short account of his life and papers see Czechoslovak Mathematical Journal 14 (89) (1964), 629 ‒ 633) contributed significantly to the development of several topics in mathematical logic. He was the first Czechoslovak mathematician to work systematically in mathematical logic; and over the years, has inspired a number of fellow-workers and students to continue in his work. The present book is the first and, regrettably, also the last monograph Rieger was to write. It is difficult to comment on those of Rieger's intentions which were not committed to paper. It appears that the book was intended to serve two purposes. First, to describe the author's concepts f mathematical logic and its character, as a whole; and, in accord with these, to present a detailed and precise exposition of several basic portions f mathematical logic, with particular attention paid to a number of important details usually passed over. And second ? and this is related to the first aim ? to describe the algebraic methods of mathematical logic. It would appear that the author had intended to confine himself mainly to methods connected with Boolean algebras. However, the text actually does not comprise the entire subject-matter that probably was intended to be considerably more extensive; the extent f the introductory chapters would then be in better proportion to the rest of the book. A practically complete manuscript, in Czech, consisting of eight chapters, was found among Rieger's papers. It seems that the author did not consider this text final and intended a thorough revision f large portions of it, mainly in the last chapters. However, it was, of course, impossible to make any essential changes or substantial additions- Some obvious minor errors have been corrected, and several editorial remarks added. The author's rather involved style raised a number of difficulties in translation, usually solved by a more or less suitable compromise. A typical aspect of this book is, in several instances, an admitted and explicit transition from concrete, intuitive and special notions to abstract, non-intuitive and general concepts. A number f these are then defined or explained several times, in different contexts and levels of generality. This instructive procedure entails other difficulties; it was attempted to alleviate these by a suitable organization of the index.