Martin's Maximum++ implies Woodin's axiom (*)

David Aspero; Ralf Schindler

doi:10.4007/annals.2021.193.3.3

Martin's Maximum⁺⁺ implies Woodin's axiom (*)

David Aspero, Ralf Schindler

Algebra, Number Theory, Logic, and Representations (ANTLR)

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

8 Citations (Scopus)

24 Downloads (Pure)

Abstract

We show that Martin's Maximum ⁺⁺ implies Woodin's Pmax axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are N2 many real numbers.

Original language	English
Pages (from-to)	793-835
Number of pages	43
Journal	Annals of Mathematics
Volume	193
Issue number	3
DOIs	https://doi.org/10.4007/annals.2021.193.3.3
Publication status	Published - May 2021

Keywords

$\mathbb P_{max}$, Continuum Hypothesis, Axiom $(*)$, forcing axioms

Access to Document

10.4007/annals.2021.193.3.3

MM++_implies_starAccepted author manuscript, 1.17 MB

Cite this

@article{4dca8d27a44b4f1ab7a74dac26e519ae,

title = "Martin's Maximum++ implies Woodin's axiom (*)",

abstract = "We show that Martin's Maximum ++ implies Woodin's Pmax axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are N2 many real numbers. ",

keywords = "$\mathbb P_{max}$, Continuum Hypothesis, Axiom $(*)$, forcing axioms",

author = "David Aspero and Ralf Schindler",

note = "Funding Information: First named author funded by EPSRC Grant EP/N032160/1. Second named author funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy EXC 2044 390685587, Mathematics M{\"u}nster: Dynamics - Geometry - Structure.",

year = "2021",

month = may,

doi = "10.4007/annals.2021.193.3.3",

language = "English",

volume = "193",

pages = "793--835",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "3",

}

TY - JOUR

T1 - Martin's Maximum++ implies Woodin's axiom (*)

AU - Aspero, David

AU - Schindler, Ralf

N1 - Funding Information: First named author funded by EPSRC Grant EP/N032160/1. Second named author funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics Münster: Dynamics - Geometry - Structure.

PY - 2021/5

Y1 - 2021/5

N2 - We show that Martin's Maximum ++ implies Woodin's Pmax axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are N2 many real numbers.

AB - We show that Martin's Maximum ++ implies Woodin's Pmax axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are N2 many real numbers.

KW - $\mathbb P_{max}$, Continuum Hypothesis, Axiom $()$, forcing axioms

UR - http://www.scopus.com/inward/record.url?scp=85114360221&partnerID=8YFLogxK

U2 - 10.4007/annals.2021.193.3.3

DO - 10.4007/annals.2021.193.3.3

M3 - Article

VL - 193

SP - 793

EP - 835

JO - Annals of Mathematics

JF - Annals of Mathematics

SN - 0003-486X

IS - 3

ER -

Martin's Maximum⁺⁺ implies Woodin's axiom (*)

Abstract

Keywords

Access to Document

Other files and links

Iterated Forcing with Side Conditions and High Forcing Axioms (DL open)

Cite this

Martin's Maximum++ implies Woodin's axiom (*)

Abstract

Keywords

Access to Document

Other files and links

Projects

Iterated Forcing with Side Conditions and High Forcing Axioms (DL open)

Cite this

Martin's Maximum⁺⁺ implies Woodin's axiom (*)