id: 03966020
dt: j
an: 03966020
au: Gerla, Giangiacomo; Vaccaro, Virginia
ti: Modal logic and model theory.
so: Stud. Log. 43, 203-216 (1984).
py: 1984
pu: Institute of Philosophy and Sociology of the Polish Academy of Sciences,
    Warsaw; Springer, Dordrecht
la: EN
cc: 
ut: first order modal logic; QS4E; rigidity axiom; completeness; compactness;
    semantics; possibility; classical model theory; existential
    completeness; infinitely generic
ci: 
li: doi:10.1007/BF02429839
ab: The authors attempt to establish a bridge between first order modal logic
    and classical model theory by means of a new modal system, QS4E,
    obtained by adding to the first order modal system QS4 a "rigidity
    axiom" scheme, $A\to LA$, where A is any basic formula, i.e., an atomic
    formula or its negation. Theorems of completeness and compactness are
    proved for QS4E. In the semantics for QS4E, possibility, MA, is
    interpreted as the possibility of extending a given model to another
    model in which A holds. This allows the authors to express some
    important concepts of classical model theory, which cannot be expressed
    in classical first order logic, e.g. existential completeness and the
    notion of being infinitely generic; and they can prove some well-known
    results of classical model theory. Since the model-theoretic concepts
    can be expressed also in $L\sb{ω\sb 1ω}$, the authors compare the
    expressive powers of this system and QS4E. Finally, the authors utilize
    the indicated relationship between modal logic and classical model
    theory in order to prove some results concerning the rigidity axiom.
rv: I.Gullvåg