First order logic without equality on relativized semantics |
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Authors: | Amitayu Banerjee Mohamed Khaled |
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Institution: | 1. Department of Logic, Institute of Philosophy, Eötvös Loránd University, Budapest, Hungary;2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary |
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Abstract: | Let be any ordinal. We consider the class of relativized diagonal free set algebras of dimension α. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class corresponds to first order logic, without equality symbol, with α-many variables and on relativized semantics. Hence, in this variation of first order logic, there is no finitely axiomatizable, complete and consistent theory. |
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Keywords: | 03G25 03G15 03B45 03C95 Free algebras Atoms Zero-dimensional elements |
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