An Intuitionistic Version of Cantor's Theorem

1996 ◽  
Vol 42 (1) ◽  
pp. 446-448 ◽  
Author(s):  
Dario Maguolo ◽  
Silvio Valentini
Keyword(s):  
Cantor’S Theorem ◽  
Intuitionistic Version

scholarly journals A constructive Galois connection between closure and interior

2012 ◽  
Vol 77 (4) ◽  
pp. 1308-1324 ◽  
Author(s):  
Francesco Ciraulo ◽  
Giovanni Sambin
Keyword(s):  
Galois Connection ◽  
Classical Correspondence ◽  
Intuitionistic Version

AbstractWe construct a Galois connection between closure and interior operators on a given set. All arguments are intuitionistically valid. Our construction is an intuitionistic version of the classical correspondence between closure and interior operators via complement.

A Game-Like Activity for Learning Cantor's Theorem

2001 ◽  
Vol 32 (2) ◽  
pp. 122
Author(s):  
Shay Gueron
Keyword(s):  
Cantor’S Theorem

scholarly journals Cantor’s Theorem in 2-Metric Spaces and its Applications to Fixed Point Problems

2011 ◽  
Vol 15 (1) ◽  
pp. 337-352 ◽  
Author(s):  
B. K. Lahiri ◽  
Pratulananda Das ◽  
Lakshmi Kanta Dey
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Problems ◽  
Cantor’S Theorem

Cantor's Theorem and Paradoxical Classes

1986 ◽  
Vol 32 (13-16) ◽  
pp. 221-226 ◽  
Author(s):  
Z. Šikić
Keyword(s):  
Cantor’S Theorem

scholarly journals Grim, omniscience, and Cantor’s theorem

1970 ◽  
Vol 17 (2) ◽  
pp. 211-223
Author(s):  
Martin Lembke
Keyword(s):  
Side Effect ◽  
Power Set ◽  
Cantor’S Theorem

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscience is sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes pre- cisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an enormously untoward side effect, but it is self-referentially incoherent as well.

scholarly journals The Refutation of Singularism?

2021 ◽  
pp. 30-52
Author(s):  
Salvatore Florio ◽  
Øystein Linnebo
Keyword(s):  
Plural Logic ◽  
Alternative Analysis ◽  
Cantor’S Theorem

Traditional analyses of plurals tended to eliminate plural expressions in favor of singular ones. These “singularist” analyses have recently faced many objections, which are intended to provide indirect support for the alternative analysis provided by plural logic. This chapter evaluates four such objections and concludes that they are less compelling than is often assumed. This conclusion is borne out by a close examination of various plural versions of Cantor’s theorem.

scholarly journals Exploring the relation between Intuitionistic BI and Boolean BI: an unexpected embedding

2009 ◽  
Vol 19 (3) ◽  
pp. 435-500 ◽  
Author(s):  
DOMINIQUE LARCHEY-WENDLING ◽  
DIDIER GALMICHE
Keyword(s):  
Representation Theorem ◽  
Separation Logic ◽  
Semantic Relations ◽  
Proof System ◽  
Kripke Semantics ◽  
Unexpected Result ◽  
Logical Implication ◽  
Logical Basis ◽  
Syntactic Constraints ◽  
Intuitionistic Version

The logic of Bunched Implications, through both its intuitionistic version (BI) and one of its classical versions, called Boolean BI (BBI), serves as a logical basis to spatial or separation logic frameworks. In BI, the logical implication is interpreted intuitionistically whereas it is generally interpreted classically in spatial or separation logics, as in BBI. In this paper, we aim to give some new insights into the semantic relations between BI and BBI. Then we propose a sound and complete syntactic constraints based framework for the Kripke semantics of both BI and BBI, a sound labelled tableau proof system for BBI, and a representation theorem relating the syntactic models of BI to those of BBI. Finally, we deduce as our main, and unexpected, result, a sound and faithful embedding of BI into BBI.

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