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

13 Citations (Scopus)

32 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

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10.4007/annals.2021.193.3.3

MM++_implies_starAccepted author manuscript, 1.17 MB

Cite this

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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.",

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PY - 2021/5

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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 (*)