Sticks and clubs

Sakaé Fuchino; Saharon Shelah; Lajos Soukup

doi:10.1016/S0168-0072(97)00030-4

Sticks and clubs

Sakaé Fuchino^*, Saharon Shelah, Lajos Soukup

^*Corresponding author for this work

Einstein Institute of Mathematics

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

26 Scopus citations

Abstract

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω₁ together with ¬CH and Martin's axiom for countable p.o.-sets.

Original language	English
Pages (from-to)	57-77
Number of pages	21
Journal	Annals of Pure and Applied Logic
Volume	90
Issue number	1-3
DOIs	https://doi.org/10.1016/S0168-0072(97)00030-4
State	Published - 15 Dec 1997

Keywords

Club principle
Preservation theorem
Stick principle
Weak Martin's axiom

Access to Document

10.1016/S0168-0072(97)00030-4

Cite this

@article{1532cbcec7e649089ec9392f4e6ee5f0,

title = "Sticks and clubs",

abstract = "We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets.",

keywords = "Club principle, Preservation theorem, Stick principle, Weak Martin's axiom",

author = "Saka{\'e} Fuchino and Saharon Shelah and Lajos Soukup",

year = "1997",

month = dec,

day = "15",

doi = "10.1016/S0168-0072(97)00030-4",

language = "אנגלית",

volume = "90",

pages = "57--77",

journal = "Annals of Pure and Applied Logic",

issn = "0168-0072",

publisher = "Elsevier B.V.",

number = "1-3",

}

TY - JOUR

T1 - Sticks and clubs

AU - Fuchino, Sakaé

AU - Shelah, Saharon

AU - Soukup, Lajos

PY - 1997/12/15

Y1 - 1997/12/15

N2 - We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets.

AB - We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω1 together with ¬CH and Martin's axiom for countable p.o.-sets.

KW - Club principle

KW - Preservation theorem

KW - Stick principle

KW - Weak Martin's axiom

UR - http://www.scopus.com/inward/record.url?scp=0031574553&partnerID=8YFLogxK

U2 - 10.1016/S0168-0072(97)00030-4

DO - 10.1016/S0168-0072(97)00030-4

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

AN - SCOPUS:0031574553

SN - 0168-0072

VL - 90

SP - 57

EP - 77

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1-3

ER -

Sticks and clubs

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this