On embedding models of arithmetic of cardinality א1 into reduced powers

Juliette Kennedy; Saharon Shelah

doi:10.4064/fm176-1-2

On embedding models of arithmetic of cardinality א₁ into reduced powers

Juliette Kennedy^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

2 Scopus citations

Abstract

In the early 1970's S. Tennenbaum proved that all countable models of PA^- + ∀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.

Original language	English
Pages (from-to)	17-24
Number of pages	8
Journal	Fundamenta Mathematicae
Volume	176
Issue number	1
DOIs	https://doi.org/10.4064/fm176-1-2
State	Published - 2003

Access to Document

10.4064/fm176-1-2

Cite this

@article{812563e2afce47b2afcccf7311afac26,

title = "On embedding models of arithmetic of cardinality א1 into reduced powers",

abstract = "In the early 1970's S. Tennenbaum proved that all countable models of PA- + ∀1 - Th(ℕ) are embeddable into the reduced product ℕω/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 Nω/D, where D is any regular filter on ω.",

author = "Juliette Kennedy and Saharon Shelah",

year = "2003",

doi = "10.4064/fm176-1-2",

language = "אנגלית",

volume = "176",

pages = "17--24",

journal = "Fundamenta Mathematicae",

issn = "0016-2736",

publisher = "Instytut Matematyczny",

number = "1",

}

TY - JOUR

T1 - On embedding models of arithmetic of cardinality א1 into reduced powers

AU - Kennedy, Juliette

AU - Shelah, Saharon

PY - 2003

Y1 - 2003

N2 - In the early 1970's S. Tennenbaum proved that all countable models of PA- + ∀1 - Th(ℕ) are embeddable into the reduced product ℕω/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 Nω/D, where D is any regular filter on ω.

AB - In the early 1970's S. Tennenbaum proved that all countable models of PA- + ∀1 - Th(ℕ) are embeddable into the reduced product ℕω/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 Nω/D, where D is any regular filter on ω.

UR - http://www.scopus.com/inward/record.url?scp=0038405065&partnerID=8YFLogxK

U2 - 10.4064/fm176-1-2

DO - 10.4064/fm176-1-2

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0038405065

SN - 0016-2736

VL - 176

SP - 17

EP - 24

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 1

ER -

On embedding models of arithmetic of cardinality א₁ into reduced powers

Abstract

Access to Document

Other files and links

Fingerprint

Cite this