Welcome to Paolo Lipparini's home page. Willkommen. Bienvenues. Benvenuti. Witajcie. ˇBienvenidos! Bem-vindos. Benibenius. Dobró požálovat’. Yo-koso. Isten hozott.

e-mail: [the first 8 letters of my family name] (a t) axp.mat.uniroma2.it
Alternative (emergency) e-mail: lpppla01 (at ) uniroma2 (dot) it

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

The suggested place for readers interested in my work is arXiv.org . There you can find recent or otherwise unpublished material and possibly extended versions of pubished material.
More quickly, you can go to zbMath or MathSciNet and look for the classification you are interested in. Journal-refs on arXiv.org are updated, too.

Here you can download some manuscripts (with a few exceptions, older material not present in arXiv), a very short curriculum (italiano, english) and slides from some talks. You can also find my contact informations, some (very disparate) links and informazioni per gli STUDENTI (only italian)

Recent works

  • Relational structures associated to topological spaces and preserved by image functions   (NOT on ArXiv!)
    (Unifies and generalizes results from A Model Theory of Topology , Contact semilattices , Universal specialization semilattices and Hypercontact semilattices , among others)

  • Non-generators in extensions of infinitary algebras  
    (NOT on ArXiv! Published on Reports on Mathematical Logic.
    This file contains an additional appendix)

  • The Tschantz and the alvin higher conditions are equivalent in congruence distributive varieties   (NOT on ArXiv! Published on Algebra Universalis)
    (Universal algebra, a 4-ary term variation on arXiv:2001.06705 )

  • The non-equivalence of two definitions of selective pseudocompactness
    (Topology; variations on pseudocompactness) (NOT on ArXiv!)

  • If every subalgebra of A^4 is congruence modular then A satisfies the tolerance identity
    $\Gamma^*\cap\Theta^*=(\Gamma\cap(\Theta\circ \Theta))^*$
    (PDF)     (DVI) (PS)
    (Universal Algebra, no assumption on the variety)
    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.

    Older manuscripts and papers.

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

  • The compactness spectrum of abstract logics, large cardinals and combinatorial principles
    (Model Theory, Set Theory, Ultrafilters)
    Bollettino U.M.I. (7) 4-B, 875-903 (1990).

  • Difference terms and commutators
    (Universal Algebra, no assumption on the variety)
    Unpublished, but occasionally quoted.
    K. Kearnes and A. Szendrei have obtained strong related results. See The relationship between two commutators .

  • Congruence identities satisfied in n-permutable varieties
    (Universal Algebra, m-permutable varieties)
    Bollettino U.M.I. (7) 8-B, 851-868 (1994).

  • About some generalizations of ($\lambda$, $\mu$)-compactness
    (Model Theory, Set Theory, Ultrafilters)
    Proceedings of the 5th Easter Conference on Model Theory (Wendisch Rietz, 1987), Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 93, 139--141 (1987).
    Reviewed here by Zentralblatt MATH.

    - Other manuscripts.

  • A new proof that n-permutable varieties satisfy lattice identities (DVI)
    (Universal Algebra, m-permutable varieties)
    This proof does not use commutator theory.

  • Addendum to "Existentially complete closure algebras"
    (Algebra, Topology)

    - In italiano.

  • Logica Matematica e valore della scienza

  • Una breve introduzione alla teoria del commutatore in algebra generale

  • Problemi matematici risolti con metodi logici

  • ETICA DEGLI AUTOVALORI

  • Il Principio dei Calzini Spaiati (in italiano, extended english summary)

  • Una breve introduzione all'algebra universale con argomenti scelti
    (versione non definitiva, ma spero gia' leggibile)


    Slides and presentations

  • Slides and abstract of the talk at Ultramath2008 , Pisa, about decomposability of ultrafilters and applications to Topology, Set Theory and Model Theory. For more details, see the AILA 2014 talk below.

  • Slides of the talk at XXIV Incontro di Logica , (Bologna february 2011) about "ordinal compactness" for topological spaces.
    More details on arXiv:1012.4737 , appeared in print in Filomat 2020, Volume 34, Issue 4, Pages: 1117-1145.

  • Slides and abstract of the talk at XXV Incontro di Logica (AILA meeting) , Pisa, 14-17 aprile 2014, about "Weak and local versions of measurability" (some inaccuracies might be present).
    More details on arXiv:1404.1586 .

  • Problems about the Jonsson distributivity spectrum , presentation for XXVI Incontro di Logica (AILA meeting) , Padova 2017.
    More details on arXiv:1702.05353 .

  • Slides of the talk at PALS Panglobal Algebra and Logic Seminar , March 2022, about "Relative lengths of Maltsev conditions".
    More details on arXiv:1902.05995 .


    Some links

  • Lettera aperta (ottobre 2016) al Presidente del Consiglio firmata da Ciro Ciliberto, Giuseppe Mingione, Giorgio Parisi e molti altri.
  • Radiorock.to the original
  • Music
  • La via matematica all'umorismo (una raccolta di barzellette matematiche molto accurata. Altri link qui)
  • ROARS sito sui problemi dell'’universitŕ e della ricerca
  • Siamo dentro la foresta. Una papera cammina, incontra un lupo...

    How to contact me

    You can write me at the following address:
    [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
    (currently retired)



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