Affiliations: Faculty of Mathematics and Natural Sciences, Cardinal
Stefan Wyszyński Uniwersity, Warsaw, Poland. E-mail:
m.krynicki@uksw.edu.pl | Department of Logic, Institute of Philosophy, Warsaw
University, Poland and Institute of Technology, University of Clermont 1.
E-mail: m.mostowski@uw.edu.pl | Institute of Mathematics, Polish Academy of Science,
Warsaw, Poland. E-mail: konrad.zdanowski@wp.pl
Abstract: The paper presents the current state of knowledge in the field of
logical investigations of finite arithmetics. This is an attempt to summarize
the ideas and results in this area. Some new results are presented –
these are mainly generalizations of the earlier results related to properties
of sl-theories and some nontrivial cases of FM-representability theorem.
