University of Leicester


"Algebras for Quantification, Substitution and Naming" Seminar Webpage

Please note: due to holiday period and absences of participants, seminar is suspended until late April mid-June. However, in the first week of June we are going to have a three days seminar with visitors inluding Jamie Gabbay and Vincenzo Ciancia, plus the whole local team involved - check in Special Events.

Future and past seminars

Seminar programme

Seminar details

Three-day seminar on nominal sets, Nominal Algebra and nominal techniques

The local team and our special guests: dr Vincenzo Ciancia and dr Murdoch "Jamie" Gabbay
June 1-3 2010, 14:00-17:00 in ATT SB2.07

Cylindric and polyadic algebras IV: bridging the gap

Dr Tadeusz Litak (University of Leicester)
Wednesday 24 March 2010, 14:30 in G4

The full impact of non-axiomatizability and non-representability theorems. Are some restricted positive results available?

Cylindric and polyadic algebras III: "one-and-a-halfth-order" logic?

Dr Tadeusz Litak (University of Leicester)
Wednesday 17 March 2010, 14:15 in G4

"Logic of schemes": what does it mean that cylindric algebras and related classes "algebraize FOL"?

Cylindric and polyadic algebras II: abstract algebras

Dr Tadeusz Litak (University of Leicester)
Wednesday 10 March 2010, 15:30 in G4

Abstract axiomatic classes. Constructing polyadic equality algebras (FPEA's or QPEA's) out of cylindric algebras: MGR (merry-go-round) identities and neat reducts. Weak and strong representation results. See the abstract of the previous talk for references, most of them with downloadable links.

Cylindric and polyadic algebras I: concrete (set) algebras

Dr Tadeusz Litak (University of Leicester)
Wednesday 24 February 2010, 15:30 in G4

This is meant to be a continuation of an introductory talk on algebraic logic I gave in January, but new participants are very welcome: I will try to make it self-contained. We will compare cylindric algebras (CA's) and polyadic equality algebras (FPEA's or QPEA's) as algebraic semantics for first-order logic. A central role will be played by operations corresponding to substitutions and permutations: term-defined in case of CA's and explicit in the signature in case of QPEA's.

Some papers I use in this presentation:

[ANS:HPLII] Hajnal Andréka, István Németi and Ildikó Sain.
Algebraic logic. Handbook of Philosophical Logic, second edition (1997). Was used extensively also in the January presentation. If you have time, have a brief look at it or perhaps even bring a copy to the seminar. Many other important papers are available here. In particular, another reference on this list I found useful was this one:
[iN:AQLIO] István Németi.
Algebraizations of quantifier logics, an introductory overview.

[jdM:ICSA00] J. Donald Monk.
An introduction to cylindric set algebras. Logic Journal of the IGPL 8 (2000), 451-506. (with an appendix by H. Andréka)
[AT:STAMS88] H. Andréka and R.J. Thompson.
A Stone Type Representation Theorem for Algebras of Relations of Higher Rank. Transactions of the American Mathematical Society 309 no.2 (1988), 671-682.
[FPACASL07] Miklós Ferenczi.
Finitary Polyadic Algebras from Cylindric Algebras. Studia Logica 87 no.1 (Oct 2007), 1-11.
[FJP:SAALSL03] Josep Maria Font, Ramon Jansana and Don Pigozzi.
A Survey of Abstract Algebraic Logic. Studia Logica 74 no.1-2 (2003), 13-97. See also update

I am also going to use a lot both volumes of the Henkin, Monk and Tarski monograph, but this one is not easily accessible in Leicester: contact me if you are interested

Author: Tadeusz Litak (tml12 if_you're_a_spambot_this_underlined_part_is_to_confuse_you at, T: +44 (0) 116 252 2593.
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