The monadic theory of ω2

DOI10.2307/2273556zbMath0549.03010OpenAlexW1956775607MaRDI QIDQ3342531

Menachem Magidor, Saharon Shelah, Yuri Gurevich

Publication date: 1983

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

Full work available at URL: https://doi.org/10.2307/2273556

zbMATH Keywords

forcingmodels of set theoryweakly compact cardinalordinalsmonadic second order theorycountable model of ZFC

Mathematics Subject Classification ID

Decidability of theories and sets of sentences (03B25) Consistency and independence results (03E35) Set-theoretic model theory (03C55)

Related Items (16)

Trees, grids, and MSO decidability: from graphs to matroids ⋮ On countable chains having decidable monadic theory ⋮ The expressive power of Malitz quantifiers for linear orderings ⋮ On decidability properties of local sentences ⋮ Notes on monadic logic. A: Monadic theory of the real line ⋮ Monadic Theory of a Linear Order Versus the Theory of its Subsets with the Lifted Min/Max Operations ⋮ Finite state automata and monadic definability of singular cardinals ⋮ Notes on monadic logic. Part B: Complexity of linear orders in ZFC ⋮ More on monadic logic. C: Monadically interpreting in stable unsuperstable \(\mathcal T\) and the monadic theory of \(^{\omega}\lambda\) ⋮ Monadic partition logics and finite automata ⋮ The monadic theory of \((\omega{}_ 2,<)\) may be complicated ⋮ Expressing cardinality quantifiers in monadic second-order logic over chains ⋮ The full binary tree cannot be interpreted in a chain ⋮ Decidable Expansions of Labelled Linear Orderings ⋮ Some problems in automata theory which depend on the models of set theory ⋮ The structure of the models of decidable monadic theories of graphs

Cites Work

• A weak generalization of MA to higher cardinals
• A new class of order types

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