Size direction games over the real line. III

Gadi Moran; Saharon Shelah

doi:10.1007/BF02764720

Size direction games over the real line. III

Gadi Moran, Saharon Shelah

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

Abstract

We prove, using the continuum hypothesis, that D (the direction player) has a winning strategy in {ie442-1} for some uncountable X, and that there is an uncountable X which intersects each perfect nowhere-dense set of reals in a countable set such that D does not win in {ie442-2} for every a. We also give another proof to the fact that Γ^S (X) is a win for D is countable.

Original language	English
Pages (from-to)	442-449
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	14
Issue number	4
DOIs	https://doi.org/10.1007/BF02764720
State	Published - Dec 1973
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/BF02764720

Cite this

@article{e707d6f08ff3494c943ae85cc67fa40a,

title = "Size direction games over the real line. III",

abstract = "We prove, using the continuum hypothesis, that D (the direction player) has a winning strategy in {ie442-1} for some uncountable X, and that there is an uncountable X which intersects each perfect nowhere-dense set of reals in a countable set such that D does not win in {ie442-2} for every a. We also give another proof to the fact that ΓS (X) is a win for D is countable.",

author = "Gadi Moran and Saharon Shelah",

year = "1973",

month = dec,

doi = "10.1007/BF02764720",

language = "English",

volume = "14",

pages = "442--449",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "4",

}

TY - JOUR

T1 - Size direction games over the real line. III

AU - Moran, Gadi

AU - Shelah, Saharon

PY - 1973/12

Y1 - 1973/12

N2 - We prove, using the continuum hypothesis, that D (the direction player) has a winning strategy in {ie442-1} for some uncountable X, and that there is an uncountable X which intersects each perfect nowhere-dense set of reals in a countable set such that D does not win in {ie442-2} for every a. We also give another proof to the fact that ΓS (X) is a win for D is countable.

AB - We prove, using the continuum hypothesis, that D (the direction player) has a winning strategy in {ie442-1} for some uncountable X, and that there is an uncountable X which intersects each perfect nowhere-dense set of reals in a countable set such that D does not win in {ie442-2} for every a. We also give another proof to the fact that ΓS (X) is a win for D is countable.

UR - http://www.scopus.com/inward/record.url?scp=51649188701&partnerID=8YFLogxK

U2 - 10.1007/BF02764720

DO - 10.1007/BF02764720

M3 - Article

AN - SCOPUS:51649188701

SN - 0021-2172

VL - 14

SP - 442

EP - 449

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 4

ER -

Size direction games over the real line. III

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this