Some remarks on Baire’s grand theorem

&
Archive for Mathematical Logic 57 (3-4):195-201 (2018)
  Copy   BIBTEX

Abstract

We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \ that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.

Categories

Add categories

Keywords

Reprint years

2017

DOI

10.1007/s00153-017-0563-6

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,881

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Decomposing baire functions.J. Cichoń, M. Morayne, J. Pawlikowski & S. Solecki - 1991 - Journal of Symbolic Logic 56 (4):1273 - 1283.
Some weak forms of the Baire category theorem.Kyriakos Kermedis - 2003 - Mathematical Logic Quarterly 49 (4):369.
On the role of the baire category theorem and dependent choice in the foundations of logic.Robert Goldblatt - 1985 - Journal of Symbolic Logic 50 (2):412-422.
Codings of separable compact subsets of the first Baire class.Pandelis Dodos - 2006 - Annals of Pure and Applied Logic 142 (1):425-441.
An analogue of the Baire category theorem.Philipp Hieronymi - 2013 - Journal of Symbolic Logic 78 (1):207-213.
A continuity principle, a version of Baire's theorem and a boundedness principle.Hajime Ishihara & Peter Schuster - 2008 - Journal of Symbolic Logic 73 (4):1354-1360.
On Countable Products of Finite Hausdorff Spaces.Horst Herrlich & Kyriakos Keremedis - 2000 - Mathematical Logic Quarterly 46 (4):537-542.
Decomposing Borel functions and structure at finite levels of the Baire hierarchy.Janusz Pawlikowski & Marcin Sabok - 2012 - Annals of Pure and Applied Logic 163 (12):1748-1764.
Baire category and nowhere differentiability for feasible functions.J. M. Breutzmann, J. H. Lutz & D. W. Juedes - 2004 - Mathematical Logic Quarterly 50 (4):460.
Some More Conservation Results on the Baire Category Theorem.Takeshi Yamazaki - 2000 - Mathematical Logic Quarterly 46 (1):105-110.
Topological framework for finite injury.Kyriakos Kontostathis - 1992 - Mathematical Logic Quarterly 38 (1):189-195.
Baire reductions and good Borel reducibilities.Luca Motto Ros - 2010 - Journal of Symbolic Logic 75 (1):323-345.
Extending Baire property by uncountably many sets.Paweł Kawa & Janusz Pawlikowski - 2010 - Journal of Symbolic Logic 75 (3):896-904.
The baire category theorem and cardinals of countable cofinality.Arnold W. Miller - 1982 - Journal of Symbolic Logic 47 (2):275-288.
Effective Borel measurability and reducibility of functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.

Analytics

Added to PP
2018-03-24

Downloads
13 (#1,036,484)

6 months
4 (#790,339)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

Playing in the first Baire class.Raphaël Carroy - 2014 - Mathematical Logic Quarterly 60 (1-2):118-132.

Add more references