Martin's Maximum${}^{++}$ implies Woodin's axiom $(*)$
David Asperó, Ralf Schindler
Abstract
We show that Martin's Maximum${}^{++}$ implies Woodin's $\mathbb{P}_{\mathrm{max}}$ 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 $ℵ_2$ many real numbers.
Topics & Concepts
AxiomMathematicsCombinatoricsSet (abstract data type)Zermelo–Fraenkel set theoryMathematical economicsAxiom of choiceDiscrete mathematicsSet theoryComputer scienceGeometryProgramming languageAdvanced Topology and Set TheoryComputability, Logic, AI AlgorithmsMathematical and Theoretical Analysis