On iterated forcing for successors of regular cardinals

Todd Eisworth

Fundamenta Mathematicae (2003)

  • Volume: 179, Issue: 3, page 249-266
  • ISSN: 0016-2736

Abstract

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We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on {δ < λ⁺: cf(δ) = λ} that complements a theorem of Shelah [4].

How to cite

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Todd Eisworth. "On iterated forcing for successors of regular cardinals." Fundamenta Mathematicae 179.3 (2003): 249-266. <http://eudml.org/doc/283038>.

@article{ToddEisworth2003,
abstract = {We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on \{δ < λ⁺: cf(δ) = λ\} that complements a theorem of Shelah [4].},
author = {Todd Eisworth},
journal = {Fundamenta Mathematicae},
keywords = {properness for larger cardinals; iterated forcing; ladder systems; uncountable support iterations; proper forcing},
language = {eng},
number = {3},
pages = {249-266},
title = {On iterated forcing for successors of regular cardinals},
url = {http://eudml.org/doc/283038},
volume = {179},
year = {2003},
}

TY - JOUR
AU - Todd Eisworth
TI - On iterated forcing for successors of regular cardinals
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 3
SP - 249
EP - 266
AB - We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on {δ < λ⁺: cf(δ) = λ} that complements a theorem of Shelah [4].
LA - eng
KW - properness for larger cardinals; iterated forcing; ladder systems; uncountable support iterations; proper forcing
UR - http://eudml.org/doc/283038
ER -

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