Vive la différence III

Saharon Shelah

doi:10.1007/s11856-008-1020-3

Vive la différence III

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

9 Scopus citations

Abstract

We show that, consistently, there is an ultrafilter ℱ on ω such that if N_n ^ℒ = (P_n^ℒ ∪ Q_n^ℒ, P_n^ℒ, Q _n^ℒ, R_n^ℒ) (for ℒ = 1, 2, n < ω), P_n^ℒ ∪ Q_n ^ℒ ⊆ ω, and ∏_{n < ω} N _n¹/ℱ ≡ ∏_{n < ω} N _n²/ℱ are models of the canonical theory t ^ind of the strong independence property, then every isomorphism from ∏_{n < ω} N_n¹/ℱ onto ∏_{n < ω} N_n²/ℱ is a product isomorphism.

Original language	English
Pages (from-to)	61-96
Number of pages	36
Journal	Israel Journal of Mathematics
Volume	166
DOIs	https://doi.org/10.1007/s11856-008-1020-3
State	Published - Aug 2008

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title = "Vive la diff{\'e}rence III",

abstract = "We show that, consistently, there is an ultrafilter ℱ on ω such that if Nn ℒ = (Pnℒ ∪ Qnℒ, Pnℒ, Q nℒ, Rnℒ) (for ℒ = 1, 2, n < ω), Pnℒ ∪ Qn ℒ ⊆ ω, and ∏n < ω N n1/ℱ ≡ ∏n < ω N n2/ℱ are models of the canonical theory t ind of the strong independence property, then every isomorphism from ∏n < ω Nn1/ℱ onto ∏n < ω Nn2/ℱ is a product isomorphism.",

author = "Saharon Shelah",

year = "2008",

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doi = "10.1007/s11856-008-1020-3",

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N2 - We show that, consistently, there is an ultrafilter ℱ on ω such that if Nn ℒ = (Pnℒ ∪ Qnℒ, Pnℒ, Q nℒ, Rnℒ) (for ℒ = 1, 2, n < ω), Pnℒ ∪ Qn ℒ ⊆ ω, and ∏n < ω N n1/ℱ ≡ ∏n < ω N n2/ℱ are models of the canonical theory t ind of the strong independence property, then every isomorphism from ∏n < ω Nn1/ℱ onto ∏n < ω Nn2/ℱ is a product isomorphism.

AB - We show that, consistently, there is an ultrafilter ℱ on ω such that if Nn ℒ = (Pnℒ ∪ Qnℒ, Pnℒ, Q nℒ, Rnℒ) (for ℒ = 1, 2, n < ω), Pnℒ ∪ Qn ℒ ⊆ ω, and ∏n < ω N n1/ℱ ≡ ∏n < ω N n2/ℱ are models of the canonical theory t ind of the strong independence property, then every isomorphism from ∏n < ω Nn1/ℱ onto ∏n < ω Nn2/ℱ is a product isomorphism.

UR - https://www.scopus.com/pages/publications/58449083907

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VL - 166

SP - 61

EP - 96

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Vive la différence III

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