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Model theory is the branch of mathematical logic which deals with the connection between a formal language and its interpretations, or models.
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Intuitionistic countermodels in which $u \leq v \implies M_u \leq M_v$
In Fitting's Intuitionistic Logic Model Theory and Forcing, the following theorem is proven:
If $X$ is a formula with no universal quantifiers and $\not\vdash_I X$, then there is a countermodel $(\ma …
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How many constant symbols can a set of intuitionistic formulas have for completeness to hold?
Fitting proves a version of the completeness theorem for intuitionistic FOL in his book on intuitionistic model theory and forcing.
Let $U$ be any set of formulas without parameters (i.e. constant sy …