Banerjee, A. and Khaled, Mohamed (2018) First order logic without equality on relativized semantics. ANNALS OF PURE AND APPLIED LOGIC, 168 (11). pp. 1227-1242. ISSN 0168-0072
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Abstract
Let α≥2 be any ordinal. We consider the class Drsα 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 Drsα are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class Drsα 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. © 2018 Elsevier B.V.
Item Type: | Article |
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Uncontrolled Keywords: | Atoms; Free algebras; Zero-dimensional elements; |
Subjects: | Q Science / természettudomány > QA Mathematics / matematika Q Science / természettudomány > QA Mathematics / matematika > QA72 Algebra / algebra |
SWORD Depositor: | MTMT SWORD |
Depositing User: | MTMT SWORD |
Date Deposited: | 16 Jan 2019 07:49 |
Last Modified: | 16 Jan 2019 07:49 |
URI: | http://real.mtak.hu/id/eprint/90014 |
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