Embedding partially ordered sets into ω ω

Ilijas Farah

Fundamenta Mathematicae (1996)

  • Volume: 151, Issue: 1, page 53-95
  • ISSN: 0016-2736

Abstract

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We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

How to cite

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Farah, Ilijas. "Embedding partially ordered sets into $^ω ω$." Fundamenta Mathematicae 151.1 (1996): 53-95. <http://eudml.org/doc/212183>.

@article{Farah1996,
abstract = {We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion $H_E$ which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).},
author = {Farah, Ilijas},
journal = {Fundamenta Mathematicae},
keywords = {embedding; game; consistency; JFM 34.0077.02; JFM 40.0446.02; partially ordered set; gaps; unbounded chains; well-ordered chains; Cohen real},
language = {eng},
number = {1},
pages = {53-95},
title = {Embedding partially ordered sets into $^ω ω$},
url = {http://eudml.org/doc/212183},
volume = {151},
year = {1996},
}

TY - JOUR
AU - Farah, Ilijas
TI - Embedding partially ordered sets into $^ω ω$
JO - Fundamenta Mathematicae
PY - 1996
VL - 151
IS - 1
SP - 53
EP - 95
AB - We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion $H_E$ which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).
LA - eng
KW - embedding; game; consistency; JFM 34.0077.02; JFM 40.0446.02; partially ordered set; gaps; unbounded chains; well-ordered chains; Cohen real
UR - http://eudml.org/doc/212183
ER -

References

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