DANGER !

In the following papers, we work in set theory without the axiom of choice, ZF.

L'axiome du choix en bande dessinée... (a comics about AC)

Commutative rings

[Mo86] Divers axiomes de choix, Séminaire d'Analyse de Clermont-Ferrand II, 1985- 1986. Abstract
[Mo87] Une forme géométrique de l'axiome de l'idéal premier, Séminaire d'Analyse de Clermont-Ferrand II, 1986-1987. Abstract

Lexicographic orders

[Mo88a] Ensembles totalement ordonnés et axiome du choix, Séminaire d'Analyse de Clermont-Ferrand II, 1987-1988. Abstract Zbl 0714.03044

Thesis

[Mo88b] Topologie, Analyse non-standard et axiome du choix, Université de Clermont-Ferrand II, Thèse de 3ième cycle, Juin 1988. Abstract

Topology of linearly ordered sets

[Ha-Mo] with L.Haddad, L'axiome de normalité pour les espaces totalement ordonnés, J. of Symbolic Logic, Vol. 55, No 1, p.277-283, 1990. Abstract
[Mo91] Extreme choices on complete lexicographic orders, Zeitschr. f. math. Logik und Grundlagen d. Math, Bd.37, S.353-355 (1991). Abstract

Measure and integration

[Mo90] Algèbres de Boole mesurées et axiome du choix, Séminaire d'Analyse de Clermont-Ferrand II, 1989-1990. Abstract
[Mo91] Algèbres de Gelfand mesurées, Séminaire d'Analyse, Université Blaise- Pascal, Clermont-Ferrand II, 1990-1991. Abstract

General topology

[Mo92] Duaux continus et axiome du choix, Séminaire d'Analyse, Université Blaise- Pascal, Clermont-Ferrand II, 1991-1992. Abstract
[Mo94] Les compacts extrêmement discontinus sont finis!, (Extremally discontinuous compact topological spaces are finite!). Semin. Anal., Univ. Blaise Pascal, Clermont II , 1993-1994, Exp. No.11, 13 p. (1994). [ISSN 0985-0732] Abstract Zbl 970.18738
[Fo-Mo] with J.Fossy, The Baire category property and some notions of compactness, Journal of the London Mathematical Society, (2) 57 (1998), 1-19. Abstract

[Mo07b]

Axiome du Choix dénombrable et compacité faible. , Exposé au séminaire ERMIT, Februar 2007.
Countable choice and compactness , Topology and Applications, Volume 155, Issue 10, (2008) Pages 1077-1088.

[Mo08c]

Uniform Eberlein spaces and the finite Axiom of Choice or arXiv preprint.
Compacité faible dans l^2(I) et axiome du choix (séminaire ERMIT, mai 2008) .
Uniform Eberlein Compactness and the Axiom of Choice, Abstract, Set Theory, Topology and Banach Spaces (Second International Topology Conference in Kielce, Poland) July 7-11, 2008.
Notions of Compactness for special subsets of IR^I and some Weak Forms of the Axiom of Choice , Journal of Symbolic Logic , Volume 75, Issue 1 (2010), 255-268.

[Rado2010] Rado's selection lemma implies Hahn-Banach, Abstract, 25th Summer Conference on Topology and its Applications, July 25-30, 2010, Kielce Poland.

Theoretical Informatics

[Bu-Mo1] with S.Burckel, Three Generators for Minimal Writing Space Computations, Theoretical Informatics and Applications , 34, 2000,131-138
[Bu-Mo2] with S.Burckel, Quadratic sequential computations of boolean mappings, Theory of Computing Systems, 37, p.519-525 (2004), pdf file.

Abstract functional analysis and Banach spaces

[Do-Mo] with J.Dodu, The Hahn-Banach property and the axiom of choice, Mathematical Logic Quarterly , 45 (3), 299-314 (1999). Abstract or pdf file
[Al-Mo] with E.Albius, Uniform smoothness entails Hahn-Banach, Quaestiones Mathematicae 24 (2001), p.425-439, Abstract or pdf file .
[De-Mo] with C.Delhommé , Dependent Choices and weak compactness, Notre-Dame Journal of Formal Logic, vol.40, No4 (1999) Abstract , download .
[Mo04] James sequences and Dependent Choices, Mathematical Logic Quarterly, vol.51, p.171-186, No2 (2005) Abstract or pdf version .
[Mo05] A new proof of James' sup theorem , preprint in arXiv (functional analysis) or published version in Extracta Mathematicae, vol.20, No 3, (2005).

[Mo07c]

The continuous Hahn-Banach property and the Axiom of Choice , talk at the ICBSOS conference (Nankai University, Tianjin, China), July 2007.
Uniform Gâteaux differentiability yields Hahn-Banach, Quaestiones Mathematicae, Volume 33, Issue 2, 2010, Pages 131-146.

[Helly09] Compactness of generalized Helly spaces , Abstract, talk at the 24th Summer Conference on Topology and Its Applications, (Brno, Czech Republic), July 2009.

Discrete mathematics

[De-Mo06] with C.Delhommé , Spanning Trees and the Axiom of Choice, Reports on Mathematical Logic, 2006, download.

[Mo08a]

Formes linéaires et axiomes de choix fini , Exposé au séminaire ERMIT, février 2008.
Puissances réduites et existence de formes linéaires , Exposé au séminaire ERMIT, septembre 2008.
Linear forms and axioms of choice, Commentationes Mathematicae Universitatis Carolinae, 50,3 (2009) 421-431.

Note de synthèse

[Mo04b] On the rôle of the Axiom of Choice in topology and functional analysis (december 2004).

Marianne Morillon