Colouring and non-productivity of א2-C.C.

Saharon Shelah

doi:10.1016/S0168-0072(96)00020-6

Colouring and non-productivity of א₂-C.C.

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

We prove that colouring of pairs from א₂ with strong properties exists. The easiest to state (and quite a well-known) problem it solves is: there are two topological spaces with cellularity א₁ whose product has cellularity א₂; equivalently, we can speak of cellularity of Boolean algebras or of Boolean algebras satisfying the א₂-c.c. whose product fails the א₂-c.c. We also deal more with guessing of clubs.

Original language	English
Pages (from-to)	153-174
Number of pages	22
Journal	Annals of Pure and Applied Logic
Volume	84
Issue number	2
DOIs	https://doi.org/10.1016/S0168-0072(96)00020-6
State	Published - 21 Mar 1997

Keywords

Cellularity
Club guessing
Colouring
Negative partition relations
Non productivity

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10.1016/S0168-0072(96)00020-6

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abstract = "We prove that colouring of pairs from א2 with strong properties exists. The easiest to state (and quite a well-known) problem it solves is: there are two topological spaces with cellularity א1 whose product has cellularity א2; equivalently, we can speak of cellularity of Boolean algebras or of Boolean algebras satisfying the א2-c.c. whose product fails the א2-c.c. We also deal more with guessing of clubs.",

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AB - We prove that colouring of pairs from א2 with strong properties exists. The easiest to state (and quite a well-known) problem it solves is: there are two topological spaces with cellularity א1 whose product has cellularity א2; equivalently, we can speak of cellularity of Boolean algebras or of Boolean algebras satisfying the א2-c.c. whose product fails the א2-c.c. We also deal more with guessing of clubs.

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KW - Club guessing

KW - Colouring

KW - Negative partition relations

KW - Non productivity

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ER -

Colouring and non-productivity of א₂-C.C.

Abstract

Keywords

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