Geodesic
On Some Applied First-Order Theories which Can Be Represented by Definitions
Bulletin of the Section of Logic, Tome 44 (2015) no. 1-2

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In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this criterion such theories as the theory of equivalence relation, the theory of partial order and many theories based on the equality relation with finite set of functional and predicate symbols are represented by definitions in the first-order predicate calculus without equality.
Keywords: theory, definition, predicate calculus 
@article{BSL_2015_44_1-2_a6,
     author = {Shalack, Vladimir},
     title = {On {Some} {Applied} {First-Order} {Theories} which {Can} {Be} {Represented} by {Definitions}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {44},
     number = {1-2},
     year = {2015},
     url = {http://geodesic.mathdoc.fr/item/BSL_2015_44_1-2_a6/}
}
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Shalack, Vladimir. On Some Applied First-Order Theories which Can Be Represented by Definitions. Bulletin of the Section of Logic, Tome 44 (2015) no. 1-2. http://geodesic.mathdoc.fr/item/BSL_2015_44_1-2_a6/