Compactness of maximal eventually different families

Eventually Different Functions and Inaccessible Cardinals

Combinatorics of Unique Maximal Factorization Families (UMFFs)

Suppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ has a unique maximal factorization over W . The classic circ-UMFF is the set of Lyndon words based on lexicographic ordering (1958). Duval (1983) designed a linear sequential Lyndon factorization algorithm; a corresponding PRA...

Common Zero Points of Two Finite Families of Maximal Monotone Operators via Proximal Point Algorithms

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...

Maximal independent families and a topological consequence

For κ ω and X a set, a familyA⊆P(X) is said to be κ-independent on X if |⋂A∈F Af (A)| κ for each F ∈ [A]<ω and f ∈ {−1,+1}F ; here A+1 =A and A−1 =X\A. Theorem 3.6. For κ ω, some A ⊆ P(κ) with |A| = 2κ is simultaneously maximal κindependent and maximal ω-independent on κ . The family A may be chosen so that every two elements of κ are separated by 2κ -many elements of A. Corollary 5.4. For κ ω ...

Martin’s Axiom and Maximal Orthogonal Families

It is shown that Martin’s Axiom for σ-centred partial orders implies that every maximal orthogonal family in R is of size 20 . For x, y ∈ R define the inner product