@article {IOPORT.05059458,
    author       = {Carter, Nathan C.},
    title        = {Reflexive intermediate propositional logics.},
    year         = {2006},
    journal      = {Notre Dame Journal of Formal Logic},
    volume       = {47},
    number       = {1},
    issn         = {0029-4527},
    pages        = {39-62},
    publisher    = {University of Notre Dame, Notre Dame, IN; Duke University Press, Durham, NC},
    doi          = {10.1305/ndjfl/1143468310},
    abstract     = {The author modifies the formulation and proof of a theorem due to {\it D. C. McCarty} [Notre Dame J. Formal Logic 43, 243--248 (2002; Zbl 1050.03041)] to get the following statement: Let $T$ be a second-order theory based on a superintuitionistic logic. If $T$ proves the completeness theorem (consistency implies existence of a model) for some superintuitionistic propositional logic, then $T$ proves every instance of $\neg\varphi\vee\neg\neg\varphi$. The proof uses very few properties of $T$ except comprehension. Defining $A= \{p\mid\neg\varphi\}\cup \{\neg p\mid\neg\neg\varphi\}$ and $B= A\cup\{p\vee\neg p\}$, $B$ is consistent since both $\{p\}$ and $\{\neg p\}$ are. By completeness, there is a model $M\models B$, hence $M\models p\vee\neg p$, so $\neg\varphi\vee\neg\neg\varphi$.},
    reviewer     = {G. E. Mints (Stanford)},
    identifier   = {05059458},
}