Studia Logica 107 (4):809-843 (2019)

Rafał Gruszczyński
Nicolaus Copernicus University
In the second installment to Gruszczyński and Pietruszczak we carry out an analysis of spaces of points of Grzegorczyk structures. At the outset we introduce notions of a concentric and \-concentric topological space and we recollect some facts proven in the first part which are important for the sequel. Theorem 2.9 is a strengthening of Theorem 5.13, as we obtain stronger conclusion weakening Tychonoff separation axiom to mere regularity. This leads to a stronger version of Theorem 6.10. Further, we show that Grzegorczyk points are maximal contracting filters in the sense of De Vries, but the converse inclusion is not necessarily true. We also compare the notions of a Grzegorczyk point and an ultrafilter, and establish several properties of topological spaces based on Grzegorczyk structures. The main results of the paper are representation and completion theorems for G-structures. We prove both set-theoretical and topological representation theorems for various classes of G-structures. We also present topological object duality theorem for the class of complete G-structures and the class of concentric spaces, both restricted to structures which satisfy countable chain condition. We conclude the paper with proving equivalence of the original Grzegorczyk axiom with the one accepted by us as axiom.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/s11225-018-9822-8
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: 60,021
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

Region-Based Topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.
Lectures on Boolean Algebras.Paul R. Halmos - 1966 - Journal of Symbolic Logic 31 (2):253-254.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Topologies and Free Constructions.Anna Bucalo & Giuseppe Rosolini - 2013 - Logic and Logical Philosophy 22 (3):327-346.
Expressive Power in First Order Topology.Paul Bankston - 1984 - Journal of Symbolic Logic 49 (2):478-487.
Aspects of General Topology in Constructive Set Theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
Aspects of General Topology in Constructive Set Theory.Peter Azcel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
The Ultrafilter Closure in ZF.Gonçalo Gutierres - 2010 - Mathematical Logic Quarterly 56 (3):331-336.
Two Topological Equivalents of the Axiom of Choice.Eric Schechter & E. Schechter - 1992 - Mathematical Logic Quarterly 38 (1):555-557.
On Turing Degrees of Points in Computable Topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.


Added to PP index

Total views
11 ( #811,422 of 2,433,513 )

Recent downloads (6 months)
1 ( #468,801 of 2,433,513 )

How can I increase my downloads?


My notes