Combinatorial functions and indecomposable cardinals

Combinatorial Functions and Indecomposable Cardinals

Combinatorial functions are used to replace indecomposable cardinals in certain types of set theoretic arguments. This allows us to extend decidability results from nonchoice set theories to set theories with a principle of linear ordering.

Compositions of Sierpiński-zygmund Functions and Related Combinatorial Cardinals

A cardinal related to compositions of Sierpiński-Zygmund functions will be considered. A combinatorial characterization of the cardinal is given and is used to answer some questions of K. Ciesielski and T. Natkaniec. It is shown that the bounding number of the continuum may be strictly smaller than continuum.

Finding p-indecomposable Functions: FCA Approach

The parametric expressibility of functions is a generalization of the expressibility via composition. All parametrically closed classes of functions (p-clones) form a lattice. For finite domains the lattice is shown to be finite, however straight-forward iteration over all functions is infeasible, and so far the p-indecomposable functions are only known for domains with two and three elements. ...

Eventually Different Functions and Inaccessible Cardinals

Lineability, Spaceability, and Additivity Cardinals for Darboux-like Functions

We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M . In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on Rn, n ≥ ...