@MISC{QC_LANG1.MIZ,
  AUTHOR = {Rudnicki, Piotr and Trybulec, Andrzej},
  TITLE = {A First Order Language},
  DAY = {08},
  MONTH = {August},
  YEAR = {1989},
  ADDRESS1 = {The University of Alberta},
  ADDRESS2 = {Warsaw University\\Bia{\l}ystok},
  SUMMARY = {In the paper a first order language is constructed. It includes
the universal quantifier and the
following propositional connectives: truth, negation, and conjunction.
The variables are divided into three kinds:
bound variables, fixed variables, and free variables. An infinite number
of predicates for each arity is provided. Schemes of structural induction
and schemes justifying definitions by structural induction have been proved.
The concept of a closed formula (a formula without free occurrences of
bound variables) is introduced.}}

