Affiliations: Insitute of Mathematics and Informatics, Opole University, Opole, Poland. jczel@math.uni.opole.pl
Correspondence:
[*]
Address for correspondence: Insitute of Mathematics and Informatics, Opole University, Opole, Poland
Abstract: The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L.
