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The theorems of beth and Craig in abstract model theory II. Compact logics

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Abstract

Various compact logics such as stationary logic, positive logic, logics with various cardinality quantifiers and cofinality quantifiers are studied. Counterexamples to the theorems of Beth and Craig are given. Back and forth arguments are studied for the first two logics, transfer theorems presented for positive logic and a new compactness proof for the confinality quantifiers is given.

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Authors and Affiliations

  1. Faculty of Computer Science, Technion (Israel Institute of Technology), Haifa, Israel

    J. A. Makowsky

  2. Department of Mathematics, Hebrew University, Jerusalem, Israel

    S. Shelah

Authors
  1. J. A. Makowsky
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  2. S. Shelah
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Supported by United States Binational Science Foundation Grant No. 1110.

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Makowsky, J.A., Shelah, S. The theorems of beth and Craig in abstract model theory II. Compact logics. Arch math Logik 21, 13–35 (1981). https://doi.org/10.1007/BF02011631

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  • DOI: https://doi.org/10.1007/BF02011631

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