Determinacy and indeterminacy of games played on complete metric spaces

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Determinacy and indeterminacy of games played on complete metric spaces. / Fishman, Lior; Ly, Tue; Simmons, David S.

In: Bulletin of the Australian Mathematical Society, Vol. 90, No. 2, 10.2014, p. 339-351.

Research output: Contribution to journalArticlepeer-review

Harvard

Fishman, L, Ly, T & Simmons, DS 2014, 'Determinacy and indeterminacy of games played on complete metric spaces', Bulletin of the Australian Mathematical Society, vol. 90, no. 2, pp. 339-351. https://doi.org/10.1017/S0004972714000069

APA

Fishman, L., Ly, T., & Simmons, D. S. (2014). Determinacy and indeterminacy of games played on complete metric spaces. Bulletin of the Australian Mathematical Society, 90(2), 339-351. https://doi.org/10.1017/S0004972714000069

Vancouver

Fishman L, Ly T, Simmons DS. Determinacy and indeterminacy of games played on complete metric spaces. Bulletin of the Australian Mathematical Society. 2014 Oct;90(2):339-351. https://doi.org/10.1017/S0004972714000069

Author

Fishman, Lior ; Ly, Tue ; Simmons, David S. / Determinacy and indeterminacy of games played on complete metric spaces. In: Bulletin of the Australian Mathematical Society. 2014 ; Vol. 90, No. 2. pp. 339-351.

Bibtex - Download

@article{7465086394ce4f04b09f712ed2cbc7ea,
title = "Determinacy and indeterminacy of games played on complete metric spaces",
abstract = "Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets.",
keywords = "math.LO",
author = "Lior Fishman and Tue Ly and Simmons, {David S.}",
note = "{\textcopyright} 2014 Australian Mathematical Publishing Association Inc. This is an author produced version of a paper accepted for publication in Bulletin of the Australian Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.",
year = "2014",
month = oct,
doi = "10.1017/S0004972714000069",
language = "English",
volume = "90",
pages = "339--351",
journal = "Bulletin of the Australian Mathematical Society",
number = "2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Determinacy and indeterminacy of games played on complete metric spaces

AU - Fishman, Lior

AU - Ly, Tue

AU - Simmons, David S.

N1 - © 2014 Australian Mathematical Publishing Association Inc. This is an author produced version of a paper accepted for publication in Bulletin of the Australian Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.

PY - 2014/10

Y1 - 2014/10

N2 - Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets.

AB - Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results have been proven using this game. In this paper we address determinacy and indeterminacy questions regarding Schmidt's game and its variations, as well as more general games played on complete metric spaces (e.g. fractals). We show that except for certain exceptional cases, these games are undetermined on Bernstein sets.

KW - math.LO

U2 - 10.1017/S0004972714000069

DO - 10.1017/S0004972714000069

M3 - Article

VL - 90

SP - 339

EP - 351

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -