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The P-ideal linking concept in critical point theory. Nonequivariant case

open access: yesThe P-ideal linking concept in critical point theory. Nonequivariant case
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p-Ideals in p-Regular Semirings

Southeast Asian Bulletin of Mathematics, 2003
Let \((S,+,\cdot)\) be an additively commutative semiring. If \((S,+)\) is an inverse semigroup, \(S\) is called inversive. The semiring \(S\) is \(p\)-regular if for each \(a\in S\) there is some \(b\in S\) such that \(na+aba=(n+1)a\) for some natural number \(n\). If \(S\) is inversive, this condition reduces to \(a+aba = 2a\). An ideal \(I\) of \(S\)
Mukhopadhyay, P.   +2 more
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L-spaces and the P-ideal dichotomy

Acta Mathematica Hungarica, 2009
\textit{S. Todorčević} [Partition problems in topology. Contemporary Mathematics, 84. Providence, RI: American Mathematical Society (AMS) (1989; Zbl 0659.54001)] proved that his principle (\(\mathcal K\)) implies that there are no strong \(L\)-spaces of countable tightness; more precisely, \((*)\): a regular space with all finite powers Lindelöf ...
Mildenberger, Heike, Zdomskyy, Lyubomyr
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P-ideal dichotomy and a strong form of the Suslin Hypothesis

Fundamenta Mathematicae, 2020
Summary: We introduce a forcing notion which forces the P-ideal dichotomy, while every almost Suslin tree from the ground model remains non-special. Thus, while the P-ideal dichotomy implies the Suslin Hypothesis, or equivalently that every Aronszajn tree has an uncountable antichain, it does not imply that every Aronszajn tree has a stationary ...
Kuzeljević, Boriša   +1 more
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p-ideals of BCI-algebras based on neutrosophic N -structures

Journal of Intelligent & Fuzzy Systems, 2021
In this paper, neutrosophic N -structures are applied to p-ideals of BCI-algebras. In fact, we introduce the notion of neutrosophic N -p-ideal in BCI-algebras, and investigate several properties. Further, we present characterizations of neutrosophic N -p-ideal.
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P-ideal dichotomy and Tukey order

Fundamenta Mathematicae
Summary: The P-ideal dichotomy is a simple and natural principle about P-ideals of countable subsets of some index set. It has proven to be particularly useful in problems involving sequential convergence in topological spaces. This is explored further here with the aim to relate it to the theory of Tukey reductions of directed sets.
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