Graduate Thesis Or Dissertation
 

Finite models of zero order propositional calculi

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  • The main result of this dissertation provides rather general conditions under which extensions of zero order propositional calculi inherit the property of having a finite characteristic model. This result is applied to show that if a calculus T is a normal extension of the Heyting calculus H, and if T has a finite characteristic model, then every normal extension of T has a finite characteristic model. Equivalent statements are shown to hold for the normal extensions of the implicational fragment of H, as well as for various extensions of the modal logics S2 and E2. Discussion of these results is preceded by a detailed study of the properties of finite order Lindenbaum models. It is followed by a summary of known results and methods on the existence or nonexistence of finite characteristic models. Finally, there is a study of completeness, which provides sufficient conditions on the first order Lindenbaum model of a calculus for the calculus to be complete. (A calculus is said to be complete if its only normal extensions are itself and the calculus in which all words are theorems.)
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