6533b872fe1ef96bd12d3113
RESEARCH PRODUCT
Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma
Janusz Czelakowskisubject
Algebra and Number TheoryForcing (recursion theory)Lindenbaum setUltrafilterFirst orderBoolean algebraTheoretical Computer ScienceFirst-order logicBoolean algebraRasiowa–Sikorski setAlgebrasymbols.namesakePerspective (geometry)substitutional semanticsComputational Theory and MathematicsforcingRasiowa–Sikorski lemmasymbolsultrafilterInformation SystemsMathematicsfirst-order logicdescription
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 .
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-12-21 | Fundamenta Informaticae |