e-mail: [the first 8 letters of my family name] (a t) axp (d ot) mat ( d ot) uniroma2 (d ot) it

My main mathematical interests are Ultrafilters, Universal Algebra, General Topology, Model Theory, Set Theory and Foundations of Mathematics.

Here you can download my most recent manuscripts and papers, as well as slides from recent talks, and some older stuff.

You can also find my contact informations, and some (very disparate) links.

For linearly ordered topological spaces, the notions of (weak) initial lambda compactness and of lambda boundedness (and hence all intermediate notions) coincide.

As a consequence, every product of initially lambda compact linearly ordered spaces is still initially lambda compact.

We characterize exactly the compactness properties of the product of kappa copies of the space of the natural numbers with the discrete topology. Some results extend to products of possibly uncountable regular cardinals with the order topology.

We introduce new compactness notions, defined in terms of order types of sequences, rather than cardinalities. Such ordinal compactness properties turn out to behave in a much more varied way, in comparison with classical cardinal compactness.

We deal particularly with spaces of small cardinality, with T

(Notice: there might be differences between the version available here and the published version. When dealing with important matters, please always refer to the published version.)

We discuss two possible ways of representing tolerances: as a homomorphic image of some congruence, and as the relational composition of some compatible relation with its converse. The relationship between these two representations are discussed.

A very simple proof is presented, showing that any tolerance on some lattice L is the image of some congruence on a subalgebra of L × L

Acta Sci. Math. (Szeged), Volume 79, Numbers 1-2, 2013.

(with Ivan Chajda, Gábor Czédli, Radomir Halas)

Algebra Universalis published online

Covering notions are exactly equivalent to accumulation notions.

Commentationes Mathematicae Universitatis Carolinae, vol. 53 (2012), issue 2, pp. 281-306

The statement in the title solves a problem by T. Retta. Incidentally, some more general results are obtained.

Czechoslovak Mathematical Journal, vol. 61, no. 3 (2011), pp. 781-784.

We introduce a covering notion which encompasses many generalizations of pseudocompactness introduced before by many authors, including Comfort, Frolik, Ginsburg, Negrepontis and Saks.

Ultrafilters are applied to the study of these notions, especially in connection with products.

Topology and its Applications Volume 158 (2011), 1655-1666.

We relativize many notions of compactness and convergence to families of subsets. Some results on pseudocompactness and D-pseudocompactness seem to be new.

Topology Proceedings, Volume 40 (2012), 29-51.

A manuscript on regularity properties of ultrafilters. Also dealing with decomposability and other stuff. It tries to survey all known results in the field.

Mathematical Logic Quarterly, Volume 56, vol. 4, pagg. 340-–374 2010.

We use Shelah's theory of possible cofinalities in order to solve some problems about ultrafilters. For example, we show that an ultrafilter is $(\lambda,\lambda)$-regular if and only if it is either $\lambda^+$-decomposable or $cf (\lambda)$-decomposable. We give applications to $[\lambda, \lambda]$-compactness of topological spaces and of abstract logics.

Notre Dame Journal of Formal Logic 49, 307--312 (2008).

We derive consequences from the existence of a term which satisfies Mal'cev identities (characterizing permutability) modulo two functions $F$ and $G$ from admissible relations to admissible relations. We also provide characterizations of varieties having a Mal'cev term modulo $F$ and $G$.

Algebra Universalis 58 (2008) 249-262.

We prove that if every subalgebra of A^2 is congruence modular then A satisfies the tolerance identity wTIP:

$\Gamma^*\cap\Theta^*=(\Gamma^*\cap \Theta)^*$.

wTIP is equivalent to Gumm's Shifting Principle.

Published in: Andretta, Alessandro; Kearnes, Keith; Zambella, Domenico (editors), Logic colloquium 2004. Cambridge University Press; Association for Symbolic Logic. Lecture Notes in Logic 29, 109-122 (2008).

Proc. Amer. Math. Soc. 136 (2008), no. 4, 1137--1144.

We show that, under certain conditions, a variety satisfies a given congruence identity if and only if it satisfies the same tolerance identity. We try to clarify the role of graphs in the study of Mal'cev conditions.

Acta Sci. Math. (Szeged) 73 (2007), 31-51

We show that if a product of topological spaces satisfies some compactness property then the factors satisfy a stronger compactness property, except for a small number of factors.

Topology and its Applications Vol 153 (9) 1365-1382 (2006).

$\Gamma^*\cap\Theta^*=(\Gamma\cap(\Theta\circ \Theta))^*$

(PDF) (DVI) (PS)

Shortened and published as: A local proof for a tolerance intersection property, Algebra Universalis Vol. 54 (3) 273-277 (2005) - external link to the published version.

(joint work with G. Czedli and E. Horvath ).

There we get Optimal Mal'tsev conditions for congruence modular varieties, we show that such varieties satisfy higher Arguesian identities and we get a very strong version of Gumm's "congruence modularity is distributivity composed with permutability".

External link to the published version, Algebra Universalis 53 (2-3) 267-279 (2005).

- Scanned from the originals (I plan to add more)

Bollettino U.M.I. (7) 4-B, 875-903 (1990).

Unpublished, but occasionally quoted.

K. Kearnes and A. Szendrei have obtained strong related results. See The relationship between two commutators .

Bollettino U.M.I. (7) 8-B, 851-868 (1994).

Proceedings of the 5

Reviewed here by Zentralblatt MATH.

- Other manuscripts.

This proof does not use commutator theory.

- In italiano.

You can write me at the following addresses:

[the first 8 letters of my second name] (a t) axp (d ot) mat ( d ot) uniroma2 (d ot) it

Dipartimento di Matematica

Universita' di Tor Vergata

Viale della Ricerca Scientifica

I-00133 ROMA

phone (office) 39-6-72594629

Arrivederci. See you. Auf Wiedersehen. Au revoir. Sayonara. Aloha. Hasta luego. Até logo. A si biri.