Abstract
This paper has two parts. In the first part (Chapters 1–4) a general method of constructing axiomatizable approximations for logics with additional quantifiers is given. The completeness theorem relative to a proper weak semantics for these approximations is proved.
In the second part (Chapters 5–8) applications of ideas from the first part are given. This part is devoted to discussions of several variants of axiomatizable approximations of logic with branched quantifiers and their strengthenings by the duality operator. These investigations are continuations of works [M. Mostowski 1987a, 1991a, 1991b].
The research work reported here has been supported by Polish Government Grant Projekt Badawczy “KWANTYFIKATORY”.
I would like to express my deep gratitude to Michal Krynicki, Dag Westerståhl, and Marek Zawadowski whose remarks to the first version of this paper were very useful for me in preparing the final version of it. Discussions of the subject with Mark Brown were very helpful, allowing me to identify some misunderstandings in my earlier work [M. Mostowski 1991a] and to eliminate them in this work.
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Mostowski, M. (1995). Quantifiers Definable by Second Order Means. In: Krynicki, M., Mostowski, M., Szczerba, L.W. (eds) Quantifiers: Logics, Models and Computation. Synthese Library, vol 249. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0524-0_10
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