Abstract
We give a general technique on how to produce counterexamples to Beth's definability (and weak definability) theorem. The method is then applied for various infinitary, cardinality quantifier logics and Δ-closure of such logics.
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The author would like to thank the United States-Israel Binational Science Foundation for partially supporting this research, and Alice Leonhardt for the beautiful typing.
This work (except 3.10 and variations) was carried out in 1975. Publication No. 113.
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Shelah, S. The theorems of Beth and craig in abstract model theory, III: Δ-logics and infinitary logics. Israel J. Math. 69, 193–213 (1990). https://doi.org/10.1007/BF02937304
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DOI: https://doi.org/10.1007/BF02937304