Second of a series of articles laying down the bases for classical first order model theory. A language is defined basically as a tuple made of an integer-valued function (adicity), a symbol of equality and a symbol for the NOR logical connective. The only requests for this tuple to be a language is that the value of the adicity in = is -2 and that its preimage (i.e. the variables set) in 0 is infinite. Existential quantification will be rendered (see [11]) by mere prefixing a formula with a letter. Then the hierarchy among symbols according to their adicity is introduced, taking advantage of attributes and clusters.The strings of symbols of a language are depth-recursively classified as terms using the standard approach (see for example [16], definition 1.1.2); technically, this is done here by deploying the ‘-multiCat' functor and the ‘unambiguous’ attribute previously introduced in [10], and the set of atomic formulas is introduced. The set of all terms is shown to be unambiguous with respect to concatenation; we say that it is a prefix set. This fact is exploited to uniquely define the subterms both of a term and of an atomic formula without resorting to a parse tree.
@article{bwmeta1.element.doi-10_2478_v10037-011-0026-1,
author = {Marco Caminati},
title = {Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms},
journal = {Formalized Mathematics},
volume = {19},
year = {2011},
pages = {169-178},
zbl = {1276.03031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0026-1}
}
Marco Caminati. Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms. Formalized Mathematics, Tome 19 (2011) pp. 169-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0026-1/
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