On embedding models of arithmetic of cardinality ℵ₁ into reduced powers

Juliette Kennedy, and Saharon Shelah. "On embedding models of arithmetic of cardinality ℵ₁ into reduced powers." Fundamenta Mathematicae 176.1 (2003): 17-24. <http://eudml.org/doc/282915>.

@article{JulietteKennedy2003,
abstract = {In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product $ℕ^ω/ℱ$, where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into $ℕ^ω/D$, where D is any regular filter on ω.},
author = {Juliette Kennedy, Saharon Shelah},
journal = {Fundamenta Mathematicae},
keywords = {Diophantine correct model; fragment of arithmetic; reduced power},
language = {eng},
number = {1},
pages = {17-24},
title = {On embedding models of arithmetic of cardinality ℵ₁ into reduced powers},
url = {http://eudml.org/doc/282915},
volume = {176},
year = {2003},
}

TY - JOUR
AU - Juliette Kennedy
AU - Saharon Shelah
TI - On embedding models of arithmetic of cardinality ℵ₁ into reduced powers
JO - Fundamenta Mathematicae
PY - 2003
VL - 176
IS - 1
SP - 17
EP - 24
AB - In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product $ℕ^ω/ℱ$, where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into $ℕ^ω/D$, where D is any regular filter on ω.
LA - eng
KW - Diophantine correct model; fragment of arithmetic; reduced power
UR - http://eudml.org/doc/282915
ER -