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Intersection
games and Bernstein sets
James Atchley, Lior Fishman and Saisneha Ghatti |
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Vol. 18 (2025), No. 5, 813–820
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Abstract |
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The Banach–Mazur game, Schmidt’s game and McMullen’s absolute game are three quintessential intersection games. We investigate their determinacy on the real line when the target set for either player is a Bernstein set — a non-Lebesgue measurable set whose construction depends on the axiom of choice. |
Keywords
logic, Banach–Mazur game, Bernstein sets, perfect sets,
games, determinacy, intersection games
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Mathematical Subject Classification
Primary: 03E25, 03E60
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Milestones
Received: 11 October 2023
Revised: 23 May 2024
Accepted: 2 June 2024
Published: 12 November 2025
Communicated by Kenneth S. Berenhaut
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Authors |
| James Atchley | |
| Department of Mathematics The University of North Texas Denton, TX United States |
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| Lior Fishman | |
| Department of Mathematics The University of North Texas Denton, TX United States |
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| Saisneha Ghatti | |
| Department of Mathematics The University of North Texas Denton, TX United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
