Review of Symbolic Logic 12 (3):405-425 (2019)

Philip Kremer
University of Toronto at Scarborough
In the topological semantics, quantified intuitionistic logic, QH, is known to be strongly complete not only for the class of all topological spaces but also for some particular topological spaces — for example, for the irrational line, ${\Bbb P}$, and for the rational line, ${\Bbb Q}$, in each case with a constant countable domain for the quantifiers. Each of ${\Bbb P}$ and ${\Bbb Q}$ is a separable zero-dimensional dense-in-itself metrizable space. The main result of the current article generalizes these known results: QH is strongly complete for any zero-dimensional dense-in-itself metrizable space with a constant domain of cardinality ≤ the space’s weight; consequently, QH is strongly complete for any separable zero-dimensional dense-in-itself metrizable space with a constant countable domain. We also prove a result that follows from earlier work of Moerdijk: if we allow varying domains for the quantifiers, then QH is strongly complete for any dense-in-itself metrizable space with countable domains.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1017/s1755020319000170
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,107
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

First Order S4 and its Measure-Theoretic Semantics.Tamar Lando - 2015 - Annals of Pure and Applied Logic 166 (2):187-218.
Quantified Modal Logic on the Rational Line.Philip Kremer - 2014 - Review of Symbolic Logic 7 (3):439-454.

View all 7 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

A Kuroda-Style J -Translation.Benno van den Berg - 2019 - Archive for Mathematical Logic 58 (5-6):627-634.
Quasi-Polish Spaces.Matthew de Brecht - 2013 - Annals of Pure and Applied Logic 164 (3):356-381.
Bi-Simulating in Bi-Intuitionistic Logic.Guillermo Badia - 2016 - Studia Logica 104 (5):1037-1050.
Geometric Possibility- an Argument From Dimension.Carolyn Brighouse - 2014 - European Journal for Philosophy of Science 4 (1):31-54.


Added to PP index

Total views
15 ( #678,400 of 2,454,632 )

Recent downloads (6 months)
1 ( #449,377 of 2,454,632 )

How can I increase my downloads?


My notes