## 39 Citations

### Proof of a conjecture of Galvin

- MathematicsForum of Mathematics, Pi
- 2020

Abstract We prove that if the set of unordered pairs of real numbers is coloured by finitely many colours, there is a set of reals homeomorphic to the rationals whose pairs have at most two colours.…

### Logic Colloquium 2006: Forcing axioms and cardinal arithmetic

- Mathematics
- 2009

We survey some recent results on the impact of strong forcing axioms such as the Proper Forcing Axiom PFA and Martin’s Maximum MM on cardinal arithmetic. We concentrate on three combinatorial…

### A family of covering properties

- Mathematics
- 2008

In the first part of this paper I present the main results of my Ph.D. thesis: several proofs of the singular cardinal hypothesis $\SCH$ are presented assuming either a strongly compact cardinal or…

### ALGEBRAIC CHARACTERIZATIONS OF MEASURE ALGEBRAS 1287 The problem of an algebraic characterization of measure algebras originated with

- Mathematics
- 2008

We present necessary and sufficient conditions for the existence of a countably additive measure on a Boolean σ-algebra. For instance, a Boolean σ-algebra B is a measure algebra if and only if B −{0}…

### L-spaces and the P-ideal dichotomy

- Mathematics
- 2009

AbstractWe extend a theorem of Todorčević: Under the assumption ($$
\mathcal{K}
$$) (see Definition 1.11), $$
\boxtimes \left\{ \begin{gathered}
any regular space Z with countable tightness such…

### L O ] 1 5 A pr 2 01 9 THE COHOMOLOGY OF THE ORDINALS I : BASIC THEORY AND CONSISTENCY

- Mathematics
- 2019

In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is Čech cohomology. We show in particular that…

### The Cohomology of the Ordinals I: Basic Theory and Consistency Results

- Mathematics
- 2019

In this paper, the first in a projected two-part series, we describe an organizing framework for the study of infinitary combinatorics. This framework is Cech cohomology. We show in particular that…

### Locally compact, $\omega_1$-compact spaces

- Mathematics
- 2017

An $\omega_1$-compact space is a space in which every closed discrete subspace is countable. We give various general conditions under which a locally compact, $\omega_1$-compact space is…

## References

SHOWING 1-8 OF 8 REFERENCES

### Making the supercompactness of κ indestructible under κ-directed closed forcing

- Mathematics
- 1978

A model is found in which there is a supercompact cardinal κ which remains supercompact in any κ-directed closed forcing extension.

### Partitioning pairs of countable ordinals

- Mathematics
- 1987

On montre que les paires d'ordinaux denombrables peuvent etre colorees avec une infinite non denombrable de couleurs de telle sorte que tout ensemble non denombrable contienne des paires de chaque…