On Depth and Depth+ of Boolean Algebras

Shimon Garti; Saharon Shelah

doi:10.1007/s00012-008-2065-1

On Depth and Depth⁺ of Boolean Algebras

Shimon Garti
, Saharon Shelah

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

3 Scopus citations

Abstract

We show that the Depth⁺ of an ultraproduct of Boolean Algebras cannot jump over the Depth⁺ of every component by more than one cardinal. Consequently we have similar results for the Depth invariant.

Original language	English
Pages (from-to)	243-248
Number of pages	6
Journal	Algebra Universalis
Volume	58
Issue number	2
DOIs	https://doi.org/10.1007/s00012-008-2065-1
State	Published - 1 Jan 2008
Externally published	Yes

Keywords

Boolean algebras
Depth
Ultraproducts

ASJC Scopus subject areas

Algebra and Number Theory
Logic

Access to Document

10.1007/s00012-008-2065-1

Cite this

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title = "On Depth and Depth+ of Boolean Algebras",

abstract = "We show that the Depth+ of an ultraproduct of Boolean Algebras cannot jump over the Depth+ of every component by more than one cardinal. Consequently we have similar results for the Depth invariant.",

keywords = "Boolean algebras, Depth, Ultraproducts",

author = "Shimon Garti and Saharon Shelah",

year = "2008",

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language = "English",

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AU - Shelah, Saharon

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AB - We show that the Depth+ of an ultraproduct of Boolean Algebras cannot jump over the Depth+ of every component by more than one cardinal. Consequently we have similar results for the Depth invariant.

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KW - Ultraproducts

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