The Hanf numbers of stationary logic. II: Comparison with other logics

DOI10.1305/NDJFL/1093636007zbMATH Open0755.03021arXivmath/9201243OpenAlexW2051358979MaRDI QIDQ1187533

Saharon Shelah

Publication date: 22 July 1992

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Abstract: We show that the ordering of the Hanf number of L_{omega, omega}(wo) (well ordering), L^c_{omega, omega} (quantification on countable sets), L_{omega, omega}(aa) (stationary logic) and second order logic, have no more restraints provable in ZFC than previously known (those independence proofs assume CON(ZFC) only). We also get results on corresponding logics for L_{lambda, mu} .

Full work available at URL: https://arxiv.org/abs/math/9201243

zbMATH Keywords

independenceZFCsecond-order logicwell orderingstationary logicHanf numberquantification on countable sets

Mathematics Subject Classification ID

Consistency and independence results (03E35) Logic with extra quantifiers and operators (03C80) Set-theoretic model theory (03C55)

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