Abstract
We give a complete axiomatization for admissible fragments ofL {ie257-1}(Q). This axiomatization implies syntactically Gregory’s characterization ofL {ie257-2} sentences with no uncountable models ([5]). This is then extended to stationary logic. To obtain these results, we employ Ressayre’s methods ([16], [17]) augmented with an application of game sentences. In section 4 we prove a result emphasizing the naturalness of Gregory’s result.
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Research supported by a grant from the National Research Council of Canada.
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Harnik, V., Makkai, M. New axiomatizations for logics with generalized quantifiers. Israel J. Math. 32, 257–281 (1979). https://doi.org/10.1007/BF02764920
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DOI: https://doi.org/10.1007/BF02764920