A dependent theory with few indiscernibles

Itay Kaplan; Saharon Shelah

doi:10.1007/s11856-014-1067-2

A dependent theory with few indiscernibles

Itay Kaplan, Saharon Shelah

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ)_T,1iff κ → (δ)_θ ^<ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

Original language	English
Pages (from-to)	59-103
Number of pages	45
Journal	Israel Journal of Mathematics
Volume	202
Issue number	1
DOIs	https://doi.org/10.1007/s11856-014-1067-2
State	Published - 2 Oct 2014

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s11856-014-1067-2

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title = "A dependent theory with few indiscernibles",

abstract = "We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ)T,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.",

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AB - We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: For every θ there is a dependent theory T of size θ such that for all κ and δ, κ → (δ)T,1iff κ → (δ)θ <ω. This means that unless there are good set theoretical reasons, there are large sets with no indiscernible sequences.

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DO - 10.1007/s11856-014-1067-2

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A dependent theory with few indiscernibles

Abstract

All Science Journal Classification (ASJC) codes

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