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

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10.1016/S0168-0072(97)00030-4

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AU - Shelah, Saharon

AU - Soukup, Lajos

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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

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

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ER -

Sticks and clubs

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Keywords

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