Logical dreams

DOI10.1090/S0273-0979-03-00981-9zbMath1024.03002arXivmath/0211398WikidataQ56040172 ScholiaQ56040172MaRDI QIDQ4804133

Saharon Shelah

Publication date: 10 April 2003

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211398

zbMATH Keywords

independenceforcinglarge cardinalsset theoryincompletenessmathematical logic

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations (03-02) Model theory (03Cxx) Set theory (03Exx)

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Mutual stationarity and singular Jonsson cardinals ⋮ Compactness in singular cardinals revisited ⋮ Between reduced powers and ultrapowers ⋮ Maddy On The Multiverse ⋮ Hierarchical multiverse of sets ⋮ Characterizations of ordinal analysis ⋮ Foundational implications of the inner model hypothesis ⋮ Forcing, Multiverse and Realism ⋮ Dependent \(T\) and existence of limit models ⋮ Multiverse Conceptions in Set Theory ⋮ Multiverse conceptions in set theory ⋮ Extender-based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis ⋮ The hyperuniverse program

Cites Work

• Many simple cardinal invariants
• On power of singular cardinals
• Rapidly growing Ramsey functions
• Proper forcing
• Inequalities for cardinal powers
• On the singular cardinals problem. II
• The axiom of determinacy, forcing axioms, and the nonstationary ideal
• More Jonsson algebras
• On nice equivalence relations on \(^\lambda 2\)
• The generalized continuum hypothesis revisited
• Existence of a \(\sigma\) finite invariant mesure for a Markov process on a locally compact space
• Classification of first order theories which have a structure theorem
• The core model
• Accessible Independence Results for Peano Arithmetic
• Chang's conjecture and powers of singular cardinals
• A note on duality between measure and category
• Filters, Cohen sets and consistent extensions of the Erdős-Dushnik-Miller Theorem
• Partition relations for cardinal numbers
• More on real-valued measurable cardinals and forcing with ideals
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