On the contributions of Helena Rasiowa to Mathematical Logic

by Josep Maria Font

Multiple-Valued Logic, an International Journal, 4 (1999) 159-179

Abstract

After an overview of the main fields of mathematical logic where Rasiowa made significant contributions, the author analyzes with some detail the philosophical basis of Rasiowa's approach to the study of mathematical logic and the main technical points that characterize her contributions.

In particular, it is shown that theses contributions are grounded on three key ideas of major Polish logicians, namely:

(1) Lindenbaum's idea of treating the set of formulas as an abstract algebra.

(2) Mostowski's idea of interpreting quantifiers as infinite conjunctions or disjunctions in the (ordered) set taken as model.

(3) Tarski's idea of defining a logic in general as a finitary closure operator on the power set of the set of formulas, completed by Los' and Suszko's notion of "structurality" (invariance under substitutions).

These ideas and Rasiowa's own constructions are described in their historical context.