#### 145 Citations

THE CONSISTENCY OF ARBITRARILY LARGE SPREAD BETWEEN THE BOUNDING AND THE SPLITTING NUMBERS

- Mathematics
- 2008

In the following κ and λ are arbitrary regular uncountable cardinals. What was known? Theorem 1 (Balcar-Pelant-Simon, [2]). It is relatively consistent with ZFC that s = ω1 < b = κ. Theorem 2… Expand

History of the Continuum in the 20th Century

- Computer Science, Mathematics
- Sets and Extensions in the Twentieth Century
- 2012

This article will trace the growing understanding of the continuum, as well as its related cardinals and associated combinatorial structures, starting at the beginning of the twentieth century and ending at the start of the twenty-first century. Expand

Combinatorics of filters and ideals

- Mathematics
- 2011

We study the combinatorial aspects of filters and ideals on count- able sets, concentrating on Borel ideals and their interaction with non-definable ones. The basic tools for this study are cardinal… Expand

Combinatorics of filters and ideals

- 2010

We study the combinatorial aspects of filters and ideals on countable sets, concentrating on Borel ideals and their interaction with non-definable ones. The basic tools for this study are cardinal… Expand

ON THE BAIRE NUMBER OF THE STONE SPACE OF [Pscr]([omega])/fin

- 1996

Throughout this paper, St(0(ω)}fin) denotes the Stone representation space of the Boolean algebra 0(ω)}fin, that is, the power set of ω modulo the ideal of finite sets. Note that St(0(ω)}fin) is the… Expand

Almost Disjoint Families and Topology

- Mathematics
- 2014

An infinite family \({\fancyscript{A}}\subset {\fancyscript{P}}(\omega )\) is almost disjoint (AD) if the intersection of any two distinct elements of \({\fancyscript{A}}\) is finite. We survey… Expand

MAD Saturated Families and SANE Player

- Mathematics
- Canadian Journal of Mathematics
- 2011

Abstract We throw some light on the question: is there a MAD family (a maximal family of infinite subsets of $\mathbb{N}$ , the intersection of any two is finite) that is saturated (=completely… Expand

Jensen's Principles and the Novak Number of Partially Ordered Sets

- Mathematics, Computer Science
- J. Symb. Log.
- 1986

Application des □ principes de Jensen a la construction d'exemples relatifs au nombre de Novak d'ensembles partiellement ordonnes

F U N D a M E N T a Mathematicae 157 (1998)

The regular open algebra of βR \ R is not equal to the completion of P(ω)/fin Abstract. Two compact spaces are co-absolute if their respective regular open algebras are isomorphic (i.e. homeomorphic… Expand