Search results for "ultrafilter"
showing 3 items of 3 documents
Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma
2017
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 .
On product of p-sequential spaces
2016
Abstract The product of finitely many regular p-compact p-sequential spaces is p-compact p-sequential for any free ultrafilter p as it follows from [5] . In the paper is produced an example of a Hausdorff p-compact p-sequential space whose square is not p-sequential. It is also given an example of a space which is sP-radial, wP-radial, vwP-radial for any P ⊂ μ ( τ ) but its square is neither sP-radial nor wP-radial nor vwP-radial space.
AC is Equivalent to the Coherence Principle. Corrigendum to my Paper "Induction Principles for Sets"
2009
Theorem 3.7 of [1] is corrected. Two coherence principles and the ultrafilter property for partial functions contained in a relation are formulated. The equivalence of the coherent principles with AC and the equivalence of the ultrafilter property with BPI is shown.