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

  • informazioni per gli STUDENTI (only italian)

    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 There you can find recent or otherwise unpublished material and possibly extended versions of pubished material.
    An updated list of published papers can be found here or using zbMath and MathSciNet. Journal-refs on arXiv.org are updated, too.

    Here you can download some manuscripts (mostly older material not present in arXiv), a very short curriculum (italiano, english) and slides from some talks. You can also find my contact informations, and some (very disparate) links.

    For all of my works, an important disclaimer is in charge, regarding possible misuses of the reference lists.

    Recent works

  • Non-generators in extensions of infinitary algebras  
    (NOT on ArXiv!)

  • 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
    $\Gamma^*\cap\Theta^*=(\Gamma\cap(\Theta\circ \Theta))^*$
    (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    Unpublished, but occasionally quoted.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


  • 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

    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.