@MISC{FOMODEL1.MIZ,
  AUTHOR = {Caminati, Marco B.},
  NOTE1 = {The author wrote this paper as part of his PhD thesis research},
  ACKNOWLEDGEMENT = {I would like to thank Marco Pedicini for his encouragement and support.},
  DAY = {29},
  MONTH = {December},
  YEAR = {2010},
  ADDRESS1 = {Mathematics Department "G.Castelnuovo"\\Sapienza University of Rome\\Piazzale Aldo Moro 5, 00185 Roma, Italy},
  TITLE = {Definition of first order language with arbitrary alphabet.
Syntax of terms, atomic formulas and their subterms.},
  SUMMARY = {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 (ie the variables set) in 0 is infinite. 
Existential quantification will be rendered (see \CITE{FOMODEL2.ABS}) 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 \CITE{pohlers1992introduction}, definition 1.1.2); technically, this is done here by deploying the `-multiCat' functor and the `unambiguous' attribute previously introduced in \CITE{FOMODEL0.ABS}, 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{pohlers1992introduction,
  title={{An introduction to mathematical logic}},
  author={Pohlers, W. and Gla{\ss}, T.},
  journal={Vorlesungsskriptum, WS},
  volume={93},
  year={1992}
}

