THE SET-THEORETIC MULTIVERSE

DOI10.1017/S1755020311000359zbMath1260.03103arXiv1108.4223OpenAlexW1972672801WikidataQ56813204 ScholiaQ56813204MaRDI QIDQ2919945

Joel David Hamkins

Publication date: 23 October 2012

Published in: The Review of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.4223

zbMATH Keywords

multiverseforcingcontinuum hypothesisaxiom of constructibility

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Set theory (03E99)

Related Items (45)

Infinite populations, choice and determinacy ⋮ ISOMORPHISM INVARIANCE AND OVERGENERATION ⋮ THE COPERNICAN MULTIVERSE OF SETS ⋮ THE MODAL LOGIC OF SET-THEORETIC POTENTIALISM AND THE POTENTIALIST MAXIMALITY PRINCIPLES ⋮ Tools, objects, and chimeras: Connes on the role of hyperreals in mathematics ⋮ Infinitesimal analysis without the axiom of choice ⋮ STEEL’S PROGRAMME: EVIDENTIAL FRAMEWORK, THE CORE AND ULTIMATE-L ⋮ RAMSIFICATION AND SEMANTIC INDETERMINACY ⋮ On the absoluteness of \(\aleph_1\)-freeness ⋮ Interview With a Set Theorist ⋮ Maddy On The Multiverse ⋮ Set Theory and Structures ⋮ Set-theoretic foundations ⋮ Forcing revisited ⋮ Hierarchical multiverse of sets ⋮ Forcing and the universe of sets: must we lose insight? ⋮ VARIETIES OF CLASS-THEORETIC POTENTIALISM ⋮ Intellectual humility in mathematics ⋮ INDEPENDENCE PROOFS IN NON-CLASSICAL SET THEORIES ⋮ A classical way forward for the regularity and normalization problems ⋮ Mathematical modality: an investigation in higher-order logic ⋮ TWO ARGUMENTS AGAINST THE GENERIC MULTIVERSE ⋮ Multiversism and Concepts of Set: How Much Relativism Is Acceptable? ⋮ Forcing, Multiverse and Realism ⋮ Category Theory and Philosophy ⋮ Multiverse Conceptions in Set Theory ⋮ On the Set-Generic Multiverse ⋮ The scope of Feferman's semi-intuitionistic set theories and his second conjecture ⋮ WHAT CAN A CATEGORICITY THEOREM TELL US? ⋮ Multiverse conceptions in set theory ⋮ BI-INTERPRETATION IN WEAK SET THEORIES ⋮ Feferman on Set Theory: Infinity up on Trial ⋮ Can we resolve the continuum hypothesis? ⋮ Maximality and ontology: how axiom content varies across philosophical frameworks ⋮ Infinite forcing and the generic multiverse ⋮ The hyperuniverse program ⋮ Arithmetic is determinate ⋮ Exploring mathematical objects from custom-tailored mathematical universes ⋮ Structural relativity and informal rigour ⋮ UNIVERSISM AND EXTENSIONS OF V ⋮ A RECONSTRUCTION OF STEEL’S MULTIVERSE PROJECT ⋮ The Significance of Relativistic Computation for the Philosophy of Mathematics ⋮ Is the dream solution of the continuum hypothesis attainable? ⋮ Naive infinitism: the case for an inconsistency approach to infinite collections ⋮ Maximal ideals in countable rings, constructively

Cites Work

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• A natural model of the multiverse axioms
• Provability interpretations of modal logic
• Certain very large cardinals are not created in small forcing extensions
• A simple maximality principle
• On the consistency strength of the inner model hypothesis
• The ground axiom is consistent with V $\neq $ HOD
• Axioms of symmetry: Throwing darts at the real number line
• Extensions with the approximation and cover properties have no new large cardinals
• The modal logic of forcing
• The ground axiom
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• Internal Consistency and the Inner Model Hypothesis
• Multiple universes of sets and indeterminate truth values

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