Definable maximal discrete sets in forcing extensions

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Definable maximal discrete sets in forcing extensions. / Schrittesser, David; Törnquist, Asger Dag.

I: Mathematical Research Letters, Bind 25, Nr. 5, 2018, s. 1591-1612.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Schrittesser, D & Törnquist, AD 2018, 'Definable maximal discrete sets in forcing extensions', Mathematical Research Letters, bind 25, nr. 5, s. 1591-1612. https://doi.org/10.4310/MRL.2018.v25.n5.a11

APA

Schrittesser, D., & Törnquist, A. D. (2018). Definable maximal discrete sets in forcing extensions. Mathematical Research Letters, 25(5), 1591-1612. https://doi.org/10.4310/MRL.2018.v25.n5.a11

Vancouver

Schrittesser D, Törnquist AD. Definable maximal discrete sets in forcing extensions. Mathematical Research Letters. 2018;25(5):1591-1612. https://doi.org/10.4310/MRL.2018.v25.n5.a11

Author

Schrittesser, David ; Törnquist, Asger Dag. / Definable maximal discrete sets in forcing extensions. I: Mathematical Research Letters. 2018 ; Bind 25, Nr. 5. s. 1591-1612.

Bibtex

@article{62ce677555524368ba3079818bff02cb,
title = "Definable maximal discrete sets in forcing extensions",
abstract = "Let  be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing that in the Sacks and Miller extensions there is a Π11 maximal orthogonal family ({"}mof{"}) of Borel probability measures on Cantor space. A similar result is also obtained for Π11 mad families. By contrast, we show that if there is a Mathias real over L then there are no Σ12 mofs.",
author = "David Schrittesser and T{\"o}rnquist, {Asger Dag}",
year = "2018",
doi = "10.4310/MRL.2018.v25.n5.a11",
language = "English",
volume = "25",
pages = "1591--1612",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "Mathematical Publishing",
number = "5",

}

RIS

TY - JOUR

T1 - Definable maximal discrete sets in forcing extensions

AU - Schrittesser, David

AU - Törnquist, Asger Dag

PY - 2018

Y1 - 2018

N2 - Let  be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing that in the Sacks and Miller extensions there is a Π11 maximal orthogonal family ("mof") of Borel probability measures on Cantor space. A similar result is also obtained for Π11 mad families. By contrast, we show that if there is a Mathias real over L then there are no Σ12 mofs.

AB - Let  be a Σ11 binary relation, and recall that a set A is -discrete if no two elements of A are related by . We show that in the Sacks and Miller forcing extensions of L there is a Δ12 maximal -discrete set. We use this to answer in the negative the main question posed in [5] by showing that in the Sacks and Miller extensions there is a Π11 maximal orthogonal family ("mof") of Borel probability measures on Cantor space. A similar result is also obtained for Π11 mad families. By contrast, we show that if there is a Mathias real over L then there are no Σ12 mofs.

U2 - 10.4310/MRL.2018.v25.n5.a11

DO - 10.4310/MRL.2018.v25.n5.a11

M3 - Journal article

VL - 25

SP - 1591

EP - 1612

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 5

ER -

ID: 184033460